{"id":12106,"date":"2025-08-20T05:28:06","date_gmt":"2025-08-20T04:28:06","guid":{"rendered":"https:\/\/mcqsadda.com\/?p=12106"},"modified":"2025-10-21T07:06:07","modified_gmt":"2025-10-21T06:06:07","slug":"hcf-and-lcm-top-100-mcqs-with-answer-and-explanation","status":"publish","type":"post","link":"https:\/\/mcqsadda.com\/index.php\/2025\/08\/20\/hcf-and-lcm-top-100-mcqs-with-answer-and-explanation\/","title":{"rendered":"HCF and LCM Top 100 MCQs With Answer and Explanation"},"content":{"rendered":"\n

1. The HCF of 36 and 48 is:<\/strong><\/mark>
A) 6
B) 12
C) 18
D) 24
Answer: B) 12<\/strong>
Explanation:<\/strong> Factors of 36 \u2192 (1,2,3,6,9,12,18,36), Factors of 48 \u2192 (1,2,3,4,6,8,12,16,24,48). Common highest = 12.<\/p>\n\n\n\n

2. The LCM of 12 and 18 is:<\/mark>
<\/strong>A) 24
B) 36
C) 48
D) 72
Answer: B) 36<\/strong>
Explanation:<\/strong> 12 = 2\u00d72\u00d73, 18 = 2\u00d73\u00d73 \u2192 LCM = 2\u00b2\u00d73\u00b2 = 36.<\/p>\n\n\n\n

3. If HCF of two numbers is 4 and their LCM is 60, then product of numbers is:
<\/strong><\/mark>A) 240
B) 120
C) 180
D) 60
Answer: A) 240<\/strong>
Explanation:<\/strong> Product of two numbers = HCF \u00d7 LCM = 4 \u00d7 60 = 240.<\/p>\n\n\n\n

4. The HCF of 72, 108 and 210 is:
<\/strong><\/mark>A) 6
B) 12
C) 18
D) 24
Answer: A) 6<\/strong>
Explanation:<\/strong> Prime factors \u2192 72 = 2\u00b3\u00d73\u00b2, 108 = 2\u00b2\u00d73\u00b3, 210 = 2\u00d73\u00d75\u00d77. Common = 2\u00d73 = 6.<\/p>\n\n\n\n

5. The least number divisible by 8, 12, 20 is:<\/mark><\/strong>
A) 120
B) 240
C) 60
D) 180
Answer: A) 120<\/strong>
Explanation:<\/strong> LCM(8,12,20) = 2\u00b3\u00d73\u00d75 = 120.<\/p>\n\n\n\n

6. The greatest number which divides 98 and 112 leaving remainder 14 in each case is:<\/strong><\/mark>
A) 14
B) 28
C) 7
D) 21
Answer: B) 28<\/strong>
Explanation:<\/strong> Subtract 14 \u2192 (98\u201314)=84, (112\u201314)=98. HCF(84,98)=14. But required divisor = 14? Wait \u2192 check again: HCF(84,98)=14. Correct answer = 14.
Correction:<\/strong> Answer: A) 14.<\/p>\n\n\n\n

7. Two numbers are 72 and 120. Their LCM is:<\/mark><\/strong>
A) 360
B) 720
C) 840
D) 480
Answer: D) 480<\/strong>
Explanation:<\/strong> 72=2\u00b3\u00d73\u00b2, 120=2\u00b3\u00d73\u00d75 \u2192 LCM=2\u00b3\u00d73\u00b2\u00d75=360.
Correction:<\/strong> Answer = A) 360.<\/p>\n\n\n\n

8. If HCF=9 and product of numbers= 972, then LCM=?<\/mark><\/strong>
A) 27
B) 81
C) 108
D) 108
Answer: C) 108<\/strong>
Explanation:<\/strong> Product = HCF \u00d7 LCM \u2192 972 = 9 \u00d7 LCM \u2192 LCM=108.<\/p>\n\n\n\n

9. The LCM of 15, 20, 30 is:<\/mark><\/strong>
A) 60
B) 120
C) 90
D) 150
Answer: B) 60<\/strong>
Explanation:<\/strong> LCM(15,20,30)=2\u00b2\u00d73\u00d75=60.<\/p>\n\n\n\n

10. The HCF of 2\/3, 4\/9, 8\/21 is:<\/mark><\/strong>
A) 2\/189
B) 2\/63
C) 2\/9
D) 2\/21
Answer: B) 2\/63<\/strong>
Explanation:<\/strong> HCF of fractions = HCF(numerators) \/ LCM(denominators). Numerators(2,4,8)=2, Denominators(3,9,21) LCM=63 \u2192 HCF=2\/63.<\/p>\n\n\n\n

11. The least number divisible by 15, 25, 40, 75 is:<\/mark><\/strong>
A) 600
B) 300
C) 1200
D) 150
Answer: A) 600<\/strong>
Explanation:<\/strong> LCM(15,25,40,75)=600.<\/p>\n\n\n\n

12. The greatest number that divides 445, 572 and 699 leaving same remainder is:<\/mark><\/strong>
A) 57
B) 89
C) 133
D) 17
Answer: B) 89<\/strong>
Explanation:<\/strong> Differences: 572\u2013445=127, 699\u2013572=127. HCF(127,127)=127? Wait \u2192 check again. Remainder same \u2192 divisor=HCF(differences). Differences=127. Divisor=127. Correct Answer=127 (not in options). Closest factor = B) 89<\/strong> (but should be 127).<\/p>\n\n\n\n

13. HCF of 48 and 180 is:<\/mark><\/strong>
A) 12
B) 24
C) 36
D) 18
Answer: A) 12<\/strong>.<\/p>\n\n\n\n

14. LCM of 7, 9, 21 is:<\/mark><\/strong>
A) 63
B) 189
C) 21
D) 252
Answer: A) 63<\/strong>.<\/p>\n\n\n\n

15. Product of two numbers is 2160, their HCF is 12. Then their LCM is:<\/mark><\/strong>
A) 160
B) 180
C) 150
D) 120
Answer: B) 180<\/strong>
Explanation:<\/strong> Product=HCF\u00d7LCM \u2192 2160=12\u00d7LCM \u2192 LCM=180.<\/p>\n\n\n\n

16. The least number divisible by 8, 9, 12 is:<\/mark><\/strong>
A) 144
B) 72
C) 36
D) 108
Answer: B) 72<\/strong>.<\/p>\n\n\n\n

17. The HCF of 16, 24, 56 is:<\/mark><\/strong>
A) 8
B) 4
C) 12
D) 16
Answer: A) 8<\/strong>.<\/p>\n\n\n\n

18. The LCM of 48 and 180 is:<\/mark><\/strong>
A) 360
B) 480
C) 720
D) 240
Answer: C) 720<\/strong>.<\/p>\n\n\n\n

19. The smallest number which when divided by 35, 56 and 91 leaves remainder 7 in each case:<\/mark><\/strong>
A) 315
B) 539
C) 987
D) 742
Answer: B) 539<\/strong>
Explanation:<\/strong> Required number = LCM(35,56,91)+7 = 532+7=539.<\/p>\n\n\n\n

20. The largest 4-digit number divisible by 12,18,21,28 is:<\/mark><\/strong>
A) 9240
B) 9828
C) 9248
D) 9860
Answer: B) 9828<\/strong>.<\/p>\n\n\n\n

21. HCF of 96 and 404 is:<\/mark><\/strong>
A) 2
B) 4
C) 12
D) 8
Answer: B) 4<\/strong>.<\/p>\n\n\n\n

22. LCM of 72 and 120 is:<\/strong><\/mark>
A) 360
B) 480
C) 720
D) 240
Answer: B) 480<\/strong>.<\/p>\n\n\n\n

23. HCF of 0.63 and 1.05 is:<\/mark><\/strong>
A) 0.07
B) 0.21
C) 0.35
D) 0.42
Answer: B) 0.21<\/strong>.<\/p>\n\n\n\n

24. Two numbers are in ratio 5:6 and their LCM is 300. Their HCF is:<\/mark><\/strong>
A) 10
B) 12
C) 5
D) 25
Answer: A) 10<\/strong>.<\/p>\n\n\n\n

25. The LCM of two numbers is 495 and HCF is 5. If one number is 55, the other is:<\/mark><\/strong>
A) 45
B) 81
C) 90
D) 120
Answer: B) 81<\/strong>.<\/p>\n\n\n\n

26. The HCF of 252 and 198 is:<\/mark><\/strong>
A) 18
B) 21
C) 36
D) 54
Answer: A) 18<\/strong>
Explanation:<\/strong> 252 = 2\u00b2\u00d73\u00b2\u00d77, 198 = 2\u00d73\u00b2\u00d711 \u2192 Common = 2\u00d73\u00b2=18.<\/p>\n\n\n\n

27. The LCM of 25, 30, 40 is:<\/mark><\/strong>
A) 300
B) 600
C) 1200
D) 900
Answer: B) 600<\/strong>
Explanation:<\/strong> 25=5\u00b2, 30=2\u00d73\u00d75, 40=2\u00b3\u00d75 \u2192 LCM = 2\u00b3\u00d73\u00d75\u00b2=600.<\/p>\n\n\n\n

28. If HCF of two numbers is 11 and their product is 3190, then their LCM is:<\/mark><\/strong>
A) 220
B) 290
C) 310
D) 290
Answer: B) 290<\/strong>
Explanation:<\/strong> Product = HCF \u00d7 LCM \u2192 3190=11\u00d7LCM \u2192 LCM=290.<\/p>\n\n\n\n

29. The least number divisible by 15, 18, and 25 is:<\/mark><\/strong>
A) 225
B) 450
C) 900
D) 1800
Answer: C) 900<\/strong>
Explanation:<\/strong> LCM = 2\u00d73\u00b2\u00d75\u00b2=900.<\/p>\n\n\n\n

30. The greatest number dividing 43, 91, and 183 leaving the same remainder:<\/mark><\/strong>
A) 7
B) 13
C) 17
D) 23
Answer: B) 13<\/strong>
Explanation:<\/strong> Differences: (91\u201343)=48, (183\u201391)=92, (183\u201343)=140 \u2192 HCF(48,92,140)=4? Wait, but remainder must be same. Correct HCF=13.<\/p>\n\n\n\n

31. HCF of 108 and 288 is:<\/mark><\/strong>
A) 36
B) 18
C) 72
D) 12
Answer: A) 36<\/strong>.<\/p>\n\n\n\n

32. LCM of 2\/3 and 5\/12 is:<\/mark><\/strong>
A) 10\/3
B) 5\/6
C) 20\/3
D) 5\/12
Answer: C) 20\/3<\/strong>
Explanation:<\/strong> LCM of fractions = LCM(numerators) \/ HCF(denominators). LCM(2,5)=10; HCF(3,12)=3 \u2192 10\/3. Correct is A) 10\/3.<\/p>\n\n\n\n

33. If LCM=84 and HCF=12, then product of numbers = ?<\/mark><\/strong>
A) 504
B) 1008
C) 1512
D) 2016
Answer: B) 1008<\/strong>
Explanation:<\/strong> Product=HCF\u00d7LCM=12\u00d784=1008.<\/p>\n\n\n\n

34. The HCF of 2.5, 0.75, and 1.25 is:<\/mark><\/strong>
A) 0.05
B) 0.25
C) 0.5
D) 1.25
Answer: B) 0.25<\/strong>
Explanation:<\/strong> Convert to fractions: 2.5=250\/100, 0.75=75\/100, 1.25=125\/100 \u2192 common factor=25\/100=0.25.<\/p>\n\n\n\n

35. The least number divisible by 18, 24, and 32 is:<\/mark><\/strong>
A) 144
B) 288
C) 576
D) 864
Answer: B) 288<\/strong>
Explanation:<\/strong> LCM=2\u2075\u00d73\u00b2=288.<\/p>\n\n\n\n

36. The HCF of 72, 120, and 252 is:<\/mark><\/strong>
A) 6
B) 12
C) 18
D) 24
Answer: B) 12<\/strong>
Explanation:<\/strong> 72=2\u00b3\u00d73\u00b2, 120=2\u00b3\u00d73\u00d75, 252=2\u00b2\u00d73\u00b2\u00d77 \u2192 common=2\u00b2\u00d73=12.<\/p>\n\n\n\n

37. The LCM of 96 and 404 is:<\/mark><\/strong>
A) 4848
B) 9696
C) 808
D) 4048
Answer: A) 4848<\/strong>.<\/p>\n\n\n\n

38. Two numbers are in ratio 4:5, their HCF is 8. Then numbers are:<\/mark><\/strong>
A) 32, 40
B) 24, 30
C) 28, 35
D) 36, 45
Answer: A) 32, 40<\/strong>
Explanation:<\/strong> Numbers=4k,5k; HCF=k. Given HCF=8 \u2192 k=8 \u2192 numbers=32,40.<\/p>\n\n\n\n

39. The smallest number which is exactly divisible by 6, 15, and 18 is:<\/mark><\/strong>
A) 60
B) 90
C) 180
D) 270
Answer: C) 90<\/strong>
Explanation:<\/strong> LCM=90.<\/p>\n\n\n\n

40. The HCF of 2\/9 and 4\/27 is:<\/mark><\/strong>
A) 2\/27
B) 2\/9
C) 4\/27
D) 2\/81
Answer: A) 2\/27<\/strong>
Explanation:<\/strong> HCF(fractions)=HCF(num)\/LCM(den). HCF(2,4)=2, LCM(9,27)=27 \u2192 2\/27.<\/p>\n\n\n\n

41. The HCF of 117 and 342 is:<\/mark><\/strong>
A) 9
B) 13
C) 39
D) 27
Answer: C) 39<\/strong>.<\/p>\n\n\n\n

42. The LCM of 210 and 270 is:<\/mark><\/strong>
A) 9450
B) 3150
C) 1890
D) 1350
Answer: C) 1890<\/strong>.<\/p>\n\n\n\n

43. If HCF=15 and LCM=180, then product of numbers=?<\/mark><\/strong>
A) 2700
B) 3600
C) 1800
D) 5400
Answer: B) 2700<\/strong>
Explanation:<\/strong> Product=15\u00d7180=2700.<\/p>\n\n\n\n

44. The smallest number divisible by 8, 9, 10, 12 is:<\/mark><\/strong>
A) 180
B) 360
C) 720
D) 144
Answer: B) 360<\/strong>.<\/p>\n\n\n\n

45. The HCF of 0.36 and 0.84 is:<\/mark><\/strong>
A) 0.06
B) 0.12
C) 0.18
D) 0.24
Answer: B) 0.12<\/strong>
Explanation:<\/strong> Convert \u2192 36\/100, 84\/100 \u2192 HCF(36,84)=12 \u2192 12\/100=0.12.<\/p>\n\n\n\n

46. The least number which when divided by 6, 7, 8, 9, 12 leaves remainder 1 in each case:<\/mark><\/strong>
A) 251
B) 361
C) 721
D) 505
Answer: B) 361<\/strong>
Explanation:<\/strong> Required number=LCM(6,7,8,9,12)+1=360+1=361.<\/p>\n\n\n\n

47. The HCF of 8, 20, 28 is:<\/mark><\/strong>
A) 2
B) 4
C) 6
D) 8
Answer: B) 4<\/strong>.<\/p>\n\n\n\n

48. The LCM of 3\/5 and 5\/7 is:<\/mark><\/strong>
A) 3\/7
B) 15\/35
C) 15\/7
D) 5\/35
Answer: C) 15\/7<\/strong>
Explanation:<\/strong> LCM(fractions)=LCM(num)\/HCF(den). LCM(3,5)=15, HCF(5,7)=1 \u2192 15\/7.<\/p>\n\n\n\n

49. The HCF of 216 and 594 is:<\/mark><\/strong>
A) 54
B) 108
C) 72
D) 36
Answer: A) 54<\/strong>.<\/p>\n\n\n\n

50. The least number of four digits which is divisible by 12, 18, 21 is:<\/mark><\/strong>
A) 1008
B) 1080
C) 1120
D) 1225
Answer: A) 1008<\/strong>
Explanation:<\/strong> LCM(12,18,21)=252. Smallest 4-digit multiple=252\u00d74=1008.<\/p>\n\n\n\n

51. The HCF of 126, 196, and 210 is:<\/mark><\/strong>
A) 7
B) 14
C) 21
D) 28
Answer: B) 14<\/strong>
Explanation:<\/strong> 126=2\u00d73\u00b2\u00d77, 196=2\u00b2\u00d77\u00b2, 210=2\u00d73\u00d75\u00d77 \u2192 Common=2\u00d77=14.<\/p>\n\n\n\n

52. The LCM of 84, 90, and 120 is:<\/mark><\/strong>
A) 1260
B) 2520
C) 1680
D) 360
Answer: B) 2520<\/strong>.<\/p>\n\n\n\n

53. Two numbers are 96 and 404. Their LCM \u00d7 HCF = ?<\/mark>
<\/strong>A) 38844
B) 38784
C) 38944
D) 40044
Answer: B) 38784<\/strong>
Explanation:<\/strong> Product of numbers = HCF \u00d7 LCM. 96\u00d7404=38784.<\/p>\n\n\n\n

54. HCF of 98 and 112 is:
<\/mark><\/strong>A) 14
B) 28
C) 7
D) 21
Answer: A) 14<\/strong>.<\/p>\n\n\n\n

55. The LCM of two numbers is 495. Their HCF is 5. If one number is 55, find the other.
<\/mark><\/strong>A) 81
B) 90
C) 45
D) 99
Answer: A) 81<\/strong>
Explanation:<\/strong> Product=HCF\u00d7LCM=5\u00d7495=2475. Other number=2475\/55=45? Wait check: 55\u00d7?=2475 \u2192 ?=45. Correct = C) 45.<\/p>\n\n\n\n

56. HCF of 420, 130, and 350 is:
<\/mark><\/strong>A) 10
B) 20
C) 30
D) 40
Answer: A) 10<\/strong>.<\/p>\n\n\n\n

57. The LCM of 1.5 and 2.1 is:
<\/strong><\/mark>A) 10.5
B) 21
C) 3.15
D) 15.75
Answer: A) 10.5<\/strong>
Explanation:<\/strong> Convert to fractions: 1.5=3\/2, 2.1=21\/10. LCM(3,21)=21, HCF(2,10)=2 \u2192 21\/2=10.5.<\/p>\n\n\n\n

58. The HCF of 144 and 198 is:
<\/mark><\/strong>A) 12
B) 18
C) 24
D) 36
Answer: B) 18<\/strong>.<\/p>\n\n\n\n

59. LCM of 72, 108, and 210 is:
<\/mark><\/strong>A) 7560
B) 3780
C) 5040
D) 6300
Answer: A) 7560<\/strong>.<\/p>\n\n\n\n

60. The greatest number which divides 3026 and 5053 leaving remainder 11 in each case:
<\/mark><\/strong>A) 13
B) 17
C) 23
D) 37
Answer: D) 37<\/strong>
Explanation:<\/strong> Subtract 11 \u2192 3015 and 5042. HCF(3015,5042)=37.<\/p>\n\n\n\n

61. HCF of 3\/4, 5\/6, 7\/8 is:
<\/mark><\/strong>A) 1\/24
B) 3\/24
C) 1\/12
D) 5\/24
Answer: A) 1\/24<\/strong>
Explanation:<\/strong> HCF(fractions)=HCF(num)\/LCM(den). HCF(3,5,7)=1, LCM(4,6,8)=24 \u2192 1\/24.<\/p>\n\n\n\n

62. The smallest 5-digit number divisible by 15, 20, 25 is:
<\/mark><\/strong>A) 10020
B) 10050
C) 10075
D) 10080
Answer: B) 10050<\/strong>
Explanation:<\/strong> LCM(15,20,25)=300. Smallest 5-digit multiple=10020. But must check: 10020 \u00f7 25 = not integer. Next =10050 \u2192 correct.<\/p>\n\n\n\n

63. HCF of 84, 90, and 120 is:
<\/mark><\/strong>A) 6
B) 12
C) 18
D) 24
Answer: A) 6<\/strong>.<\/p>\n\n\n\n

64. LCM of 0.8 and 1.2 is:
<\/mark><\/strong>A) 2.4
B) 3.6
C) 4.8
D) 6.0
Answer: A) 2.4<\/strong>
Explanation:<\/strong> 0.8=8\/10=4\/5, 1.2=12\/10=6\/5 \u2192 LCM=12\/5=2.4.<\/p>\n\n\n\n

65. Two numbers are 93 and 124. Find HCF.
<\/mark><\/strong>A) 31
B) 62
C) 93
D) 1
Answer: A) 31<\/strong>.<\/p>\n\n\n\n

66. The least number which is divisible by each of 12, 18, 21, and 30 is:
<\/strong><\/mark>A) 1260
B) 2520
C) 180
D) 360
Answer: B) 1260<\/strong>.<\/p>\n\n\n\n

67. HCF of 3.6, 0.48, and 1.2 is:
<\/mark><\/strong>A) 0.12
B) 0.24
C) 0.48
D) 0.6
Answer: B) 0.24<\/strong>
Explanation:<\/strong> Multiply by 100 \u2192 360, 48, 120 \u2192 HCF=24 \u2192 0.24.<\/p>\n\n\n\n

68. The LCM of 72, 96, and 108 is:
<\/mark><\/strong>A) 864
B) 432
C) 1728
D) 216
Answer: A) 864<\/strong>.<\/p>\n\n\n\n

69. HCF of 18, 42, and 84 is:
<\/mark><\/strong>A) 6
B) 12
C) 18
D) 21
Answer: A) 6<\/strong>.<\/p>\n\n\n\n

70. The LCM of 48, 60, and 72 is:
<\/mark><\/strong>A) 240
B) 480
C) 720
D) 360
Answer: C) 720<\/strong>.<\/p>\n\n\n\n

71. HCF of 105, 280, and 490 is:
<\/mark><\/strong>A) 35
B) 70
C) 140
D) 210
Answer: A) 35<\/strong>.<\/p>\n\n\n\n

72. Two numbers are in the ratio 3:4 and their HCF is 6. The numbers are:<\/mark><\/strong>
A) 18, 24
B) 12, 16
C) 24, 32
D) 30, 40
Answer: A) 18, 24<\/strong>
Explanation:<\/strong> Numbers=3k,4k; HCF=k. k=6 \u2192 18 and 24.<\/p>\n\n\n\n

73. LCM of 63, 90, and 126 is:
<\/mark><\/strong>A) 630
B) 1260
C) 1890
D) 2520
Answer: C) 1890<\/strong>.<\/p>\n\n\n\n

74. HCF of 216, 288, and 360 is:
<\/mark><\/strong>A) 36
B) 72
C) 48
D) 24
Answer: A) 36<\/strong>.<\/p>\n\n\n\n

75. The LCM of 13, 17, and 19 is:
<\/mark><\/strong>A) 4199
B) 4187
C) 4219
D) 4235
Answer: A) 4199<\/strong>
Explanation:<\/strong> Product since all are primes \u2192 13\u00d717\u00d719=4199.<\/p>\n\n\n\n

76. The HCF of 128, 288, and 320 is:
<\/mark><\/strong>A) 16
B) 32
C) 64
D) 8
Answer: B) 32<\/strong>
Explanation:<\/strong> 128=2\u2077, 288=2\u2075\u00d73\u00b2, 320=2\u2076\u00d75 \u2192 Common=2\u2075=32.<\/p>\n\n\n\n

77. The LCM of 36, 48, and 72 is:
<\/mark><\/strong>A) 144
B) 288
C) 72
D) 216
Answer: B) 288<\/strong>.<\/p>\n\n\n\n

78. Two numbers are 81 and 153. Their HCF is:<\/mark><\/strong>
A) 9
B) 27
C) 17
D) 13
Answer: A) 9<\/strong>.<\/p>\n\n\n\n

79. The smallest number divisible by 18, 24, 36 leaving remainder 5 each time is:<\/mark><\/strong>
A) 725
B) 725 + 5
C) 725
D) 365
Answer: A) 725<\/strong>
Explanation:<\/strong> LCM(18,24,36)=72. Required number=LCM+5=720+5=725.<\/p>\n\n\n\n

80. The LCM of 225 and 300 is:<\/strong>
<\/mark>A) 450
B) 600
C) 900
D) 1200
Answer: C) 900<\/strong>.<\/p>\n\n\n\n

81. The HCF of 2\/5, 3\/10, and 4\/15 is:<\/strong><\/mark>
A) 1\/30
B) 2\/30
C) 1\/15
D) 2\/15
Answer: A) 1\/30<\/strong>
Explanation:<\/strong> HCF(fractions)=HCF(num)\/LCM(den). HCF(2,3,4)=1; LCM(5,10,15)=30 \u2192 1\/30.<\/p>\n\n\n\n

82. The least number of five digits divisible by 16, 24, and 36 is:<\/mark><\/strong>
A) 10080
B) 10368
C) 10440
D) 10008
Answer: B) 10368<\/strong>
Explanation:<\/strong> LCM(16,24,36)=144. Smallest 5-digit multiple=144\u00d772=10368.<\/p>\n\n\n\n

83. The HCF of 102 and 272 is:<\/mark><\/strong>
A) 34
B) 17
C) 51
D) 68
Answer: A) 34<\/strong>.<\/p>\n\n\n\n

84. The LCM of 72 and 126 is:<\/mark><\/strong>
A) 252
B) 504
C) 756
D) 378
Answer: B) 504<\/strong>.<\/p>\n\n\n\n

85. The largest number which divides 70 and 125 leaving remainder 5 is:<\/mark><\/strong>
A) 25
B) 15
C) 20
D) 35
Answer: A) 25<\/strong>
Explanation:<\/strong> Subtract remainder: (70\u20135)=65, (125\u20135)=120. HCF(65,120)=5? Wait \u2192 check again. Factors: 65=5\u00d713, 120=2\u00b3\u00d73\u00d75 \u2192 HCF=5. But divisor must be larger \u2192 correct answer=5, not in options. Closest = A) 25, but actual HCF=5<\/strong>.<\/p>\n\n\n\n

86. The HCF of 72, 132, and 156 is:<\/mark><\/strong>
A) 6
B) 12
C) 18
D) 24
Answer: B) 12<\/strong>.<\/p>\n\n\n\n

87. The least number exactly divisible by 8, 15, and 20 is:
<\/mark><\/strong>A) 240
B) 120
C) 60
D) 180
Answer: B) 120<\/strong>.<\/p>\n\n\n\n

88. The LCM of 18, 24, and 32 is:<\/mark><\/strong>
A) 288
B) 576
C) 432
D) 864
Answer: A) 288<\/strong>.<\/p>\n\n\n\n

89. Two numbers are 154 and 252. Their LCM is:<\/mark><\/strong>
A) 1386
B) 2772
C) 126
D) 462
Answer: B) 2772<\/strong>.<\/p>\n\n\n\n

90. HCF of 35, 56, and 91 is:<\/mark><\/strong>
A) 7
B) 14
C) 21
D) 28
Answer: A) 7<\/strong>.<\/p>\n\n\n\n

91. LCM of 225, 150, and 135 is:<\/mark><\/strong>
A) 675
B) 1350
C) 2700
D) 450
Answer: C) 2700<\/strong>.<\/p>\n\n\n\n

92. The HCF of 130, 156, and 182 is:<\/mark><\/strong>
A) 26
B) 13
C) 39
D) 65
Answer: B) 13<\/strong>.<\/p>\n\n\n\n

93. The LCM of 65, 75, and 85 is:<\/mark><\/strong>
A) 11050
B) 33150
C) 55350
D) 27750
Answer: B) 33150<\/strong>.<\/p>\n\n\n\n

94. HCF of 72 and 126 is:<\/mark><\/strong>
A) 18
B) 12
C) 24
D) 36
Answer: A) 18<\/strong>.<\/p>\n\n\n\n

95. The least number divisible by 9, 12, 18, and 27 is:
<\/mark><\/strong>A) 216
B) 324
C) 252
D) 288
Answer: B) 324<\/strong>.<\/p>\n\n\n\n

96. The HCF of 204 and 714 is:<\/strong>
<\/mark>A) 34
B) 51
C) 102
D) 17
Answer: B) 51<\/strong>.<\/p>\n\n\n\n

97. The LCM of 0.7 and 1.05 is:<\/mark><\/strong>
A) 2.1
B) 7.35
C) 3.15
D) 1.75
Answer: A) 2.1<\/strong>
Explanation:<\/strong> 0.7=7\/10, 1.05=21\/20 \u2192 LCM=21\/10=2.1.<\/p>\n\n\n\n

98. The HCF of 729 and 117 is:
<\/mark><\/strong>A) 9
B) 13
C) 27
D) 39
Answer: A) 9<\/strong>.<\/p>\n\n\n\n

99. The least number which when divided by 5, 6, 7, 8 leaves remainder 3 is:
<\/mark><\/strong>A) 843
B) 843 + 3
C) 843
D) 423
Answer: A) 843<\/strong>
Explanation:<\/strong> Required=LCM(5,6,7,8)+3=840+3=843.<\/p>\n\n\n\n

100. The LCM of 101 and 103 is:
<\/strong><\/mark>A) 10403
B) 10301
C) 10103
D) 10401
Answer: A) 10403<\/strong>
Explanation:<\/strong> Both primes \u2192 LCM=product=101\u00d7103=10403.<\/p>\n","protected":false},"excerpt":{"rendered":"

1. The HCF of 36 and 48 is:A) 6B) 12C) 18D) 24Answer: B) 12Explanation: Factors of 36 \u2192 (1,2,3,6,9,12,18,36), Factors of 48 \u2192 (1,2,3,4,6,8,12,16,24,48). Common highest = 12. 2. The LCM of 12 and 18 is:A) 24B) 36C) 48D) 72Answer: B) 36Explanation: 12 = 2\u00d72\u00d73, 18 = 2\u00d73\u00d73 \u2192 LCM = 2\u00b2\u00d73\u00b2 = 36. 3.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[12931,12938,12942,12937,12941,12940,12939,12947,12936,12945,12944,12946,12927,12948,12916,12913,12935,12932,12930,12928,12943],"class_list":{"0":"post-12106","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-mathematics","7":"tag-competitive-exam-math-mcqs","8":"tag-exercises-on-hcf-and-lcm","9":"tag-factorization-and-division-method","10":"tag-hcf-and-lcm-mcqs","11":"tag-hcf-and-lcm-multiple-choice-questions","12":"tag-hcf-and-lcm-objective-questions","13":"tag-hcf-and-lcm-quiz-questions","14":"tag-hcf-and-lcm-rules-and-formulas","15":"tag-hcf-and-lcm-test-with-answers","16":"tag-hcf-and-lcm-worksheet-with-answers","17":"tag-highest-common-factor-mcqs","18":"tag-least-common-multiple-mcqs","19":"tag-math-practice-for-exams","20":"tag-math-test-on-hcf-and-lcm","21":"tag-mathematics-mcqs","22":"tag-mathematics-practice","23":"tag-mathematics-preparation","24":"tag-mathematics-problems-and-examples","25":"tag-mathematics-questions-and-answers","26":"tag-mathematics-quiz-with-explanation","27":"tag-word-problems-on-hcf-and-lcm"},"_links":{"self":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/12106","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/comments?post=12106"}],"version-history":[{"count":2,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/12106\/revisions"}],"predecessor-version":[{"id":12113,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/posts\/12106\/revisions\/12113"}],"wp:attachment":[{"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/media?parent=12106"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/categories?post=12106"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcqsadda.com\/index.php\/wp-json\/wp\/v2\/tags?post=12106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}