LCM, Remainder & Divisibility Practice Questions with Answers

Solve These Questions

1. Two bells ring every 16 minutes and 24 minutes. After how many minutes will they ring together again?
   Answer: 48 minutes
2. A number leaves remainder 4 when divided by 9, 12, and 15. Find the smallest such number.
   Answer: 4
3. A bus arrives every 18 minutes and another every 30 minutes. When will they arrive together again?
   Answer: 90 minutes
4. A number leaves remainder 3 when divided by 7 and remainder 5 when divided by 9. Find the smallest such number.
   Answer: 59
5. Three lights blink every 8 seconds, 12 seconds, and 16 seconds. After how many seconds will they blink together again?
   Answer: 48 seconds
6. A number leaves remainder 2 when divided by 6 and remainder 4 when divided by 11. Find the smallest such number.
   Answer: 26
7. Riya visits a park every 6 days and Ananya every 15 days. After how many days will they visit together again?
   Answer: 30 days
8. A number leaves remainder 5 when divided by 8 and remainder 7 when divided by 10. Find the smallest such number.
   Answer: 37
9. Two trains leave a station every 20 minutes and 30 minutes. After how many minutes will they leave together again?
   Answer: 60 minutes
10. A number leaves remainder 6 when divided by 11 and remainder 8 when divided by 13. Find the smallest such number.
    Answer: 138
11. Three bells ring every 12 minutes, 18 minutes, and 24 minutes. When will they ring together again?
    Answer: 72 minutes
12. A number leaves remainder 3 when divided by 5 and remainder 4 when divided by 7. Find the smallest such number.
    Answer: 18
13. Two machines complete a cycle every 15 minutes and 25 minutes. After how many minutes will they complete a cycle together again?
    Answer: 75 minutes
14. A number leaves remainder 7 when divided by 12, 18, and 24. Find the smallest such number.
    Answer: 7
15. Two alarms ring every 18 minutes and 27 minutes. After how many minutes will they ring together again?
    Answer: 54 minutes
16. A number leaves remainder 1 when divided by 6 and remainder 4 when divided by 9. Find the smallest such number.
    Answer: 13
17. Three buses arrive every 10 minutes, 15 minutes, and 25 minutes. When will all three arrive together again?
    Answer: 150 minutes
18. A number leaves remainder 5 when divided by 9 and remainder 8 when divided by 11. Find the smallest such number.
    Answer: 41
19. Two sprinklers operate every 16 minutes and 24 minutes. After how many minutes will they operate together again?
    Answer: 48 minutes
20. A number leaves remainder 2 when divided by 7 and remainder 6 when divided by 10. Find the smallest such number.
    Answer: 16
21. Two workers take breaks every 20 minutes and 45 minutes. After how many minutes will they take a break together again?
    Answer: 180 minutes
22. A number leaves remainder 4 when divided by 10, 15, and 20. Find the smallest such number.
    Answer: 4
23. Three lights flash every 9 seconds, 15 seconds, and 18 seconds. When will all three flash together again?
    Answer: 90 seconds
24. A number leaves remainder 3 when divided by 8 and remainder 6 when divided by 11. Find the smallest such number.
    Answer: 83
25. Two trains arrive every 24 minutes and 40 minutes. After how many minutes will they arrive together again?
    Answer: 120 minutes
26. A number leaves remainder 5 when divided by 12 and remainder 7 when divided by 13. Find the smallest such number.
    Answer: 137
27. Three students practice every 8 days, 12 days, and 20 days. After how many days will they practice together again?
    Answer: 120 days
28. A number leaves remainder 2 when divided by 9, remainder 3 when divided by 10, and remainder 4 when divided by 11. Find the smallest such number.
    Answer: 983
29. Two clocks chime every 21 minutes and 28 minutes. When will they chime together again?
    Answer: 84 minutes
30. A number leaves remainder 6 when divided by 14, 21, and 28. Find the smallest such number.
    Answer: 6
31. Two buses leave every 25 minutes and 35 minutes. After how many minutes will they leave together again?
    Answer: 175 minutes
32. A number leaves remainder 1 when divided by 5 and remainder 3 when divided by 8. Find the smallest such number.
    Answer: 11
33. Three bells ring every 15 minutes, 20 minutes, and 30 minutes. When will they ring together again?
    Answer: 60 minutes
34. A number leaves remainder 4 when divided by 7 and remainder 2 when divided by 9. Find the smallest such number.
    Answer: 11
35. Two machines are serviced every 30 days and 45 days. After how many days will they be serviced together again?
    Answer: 90 days
36. A number leaves remainder 5 when divided by 11 and remainder 9 when divided by 13. Find the smallest such number.
    Answer: 126
37. Three buses arrive every 14 minutes, 21 minutes, and 28 minutes. When will all three arrive together again?
    Answer: 84 minutes
38. A number leaves remainder 3 when divided by 6, remainder 4 when divided by 8, and remainder 5 when divided by 10. Find the smallest such number.
    Answer: No solution
39. Two athletes train every 12 days and 18 days. After how many days will they train together again?
    Answer: 36 days
40. A number leaves remainder 7 when divided by 15 and remainder 9 when divided by 16. Find the smallest such number.
    Answer: 217
41. Two alarms sound every 22 minutes and 33 minutes. After how many minutes will they sound together again?
    Answer: 66 minutes
42. A number leaves remainder 2 when divided by 5, remainder 3 when divided by 7, and remainder 4 when divided by 9. Find the smallest such number.
    Answer: 157
43. Three machines complete their cycles every 12 minutes, 16 minutes, and 20 minutes. After how many minutes will all complete a cycle together?
    Answer: 240 minutes
44. A number leaves remainder 5 when divided by 8, remainder 7 when divided by 11, and remainder 9 when divided by 13. Find the smallest such number.
    Answer: 997
45. Two school bells ring every 24 minutes and 36 minutes. When will they ring together again?
    Answer: 72 minutes
46. A number leaves remainder 4 when divided by 9 and remainder 7 when divided by 12. Find the smallest such number.
    Answer: 31
47. Three lights change every 20 seconds, 30 seconds, and 45 seconds. After how many seconds will they change together again?
    Answer: 180 seconds
48. A number leaves remainder 3 when divided by 10, remainder 5 when divided by 12, and remainder 7 when divided by 14. Find the smallest such number.
    Answer: 413
49. Two trains leave every 28 minutes and 42 minutes. After how many minutes will they leave together again?
    Answer: 84 minutes
50. A number leaves remainder 6 when divided by 13 and remainder 8 when divided by 15. Find the smallest such number.
    Answer: 188
51. Three bells ring every 18 minutes, 24 minutes, and 30 minutes. After how many minutes will they ring together again?
    Answer: 360 minutes
52. A number leaves remainder 5 when divided by 12, 18, and 24. Find the smallest such number.
    Answer: 5
53. Two buses arrive every 24 minutes and 36 minutes. After how many minutes will they arrive together again?
    Answer: 72 minutes
54. A number leaves remainder 7 when divided by 11 and remainder 3 when divided by 14. Find the smallest such number.
    Answer: 73
55. Three lights blink every 12 seconds, 18 seconds, and 30 seconds. After how many seconds will they blink together again?
    Answer: 180 seconds
56. A number leaves remainder 4 when divided by 9 and remainder 7 when divided by 13. Find the smallest such number.
    Answer: 85
57. Three students visit the library every 12 days, 18 days, and 30 days. After how many days will they visit together again?
    Answer: 180 days
58. A number leaves remainder 6 when divided by 14 and remainder 9 when divided by 17. Find the smallest such number.
    Answer: 230
59. Two machines complete cycles every 28 minutes and 42 minutes. After how many minutes will they complete a cycle together again?
    Answer: 84 minutes
60. Find the least 4-digit number exactly divisible by 16, 24, and 32.
    Answer: 1056
61. Find the least 5-digit number exactly divisible by 24, 36, and 48.
    Answer: 10080
62. Find the least 6-digit number exactly divisible by 48, 64, and 96.
    Answer: 100032
63. Find the least 4-digit number exactly divisible by 30, 45, and 60.
    Answer: 1080
64. Find the least 4-digit number exactly divisible by 32 and 48.
    Answer: 1056
65. Find the least 5-digit number which is exactly divisible by 18, 24, and 40.
    Answer: 10080
66. Find the least 5-digit number which is exactly divisible by 22, 33, and 44.
    Answer: 10032
67. Find the least 4-digit number which is exactly divisible by 26, 39, and 52.
    Answer: 1092
68. Find the least 4-digit number which is exactly divisible by 27, 36, and 54.
    Answer: 1080
69. Find the least 6-digit number which is exactly divisible by 28, 35, and 70.
    Answer: 100100
70. Find the smallest 4-digit number exactly divisible by 12, 18, and 24.
    Answer: 1008
71. Find the smallest 5-digit number exactly divisible by 15, 20, and 30.
    Answer: 10020
72. Find the smallest 6-digit number exactly divisible by 18, 24, and 36.
    Answer: 100008
73. Find the smallest 4-digit number exactly divisible by 16, 20, and 40.
    Answer: 1040
74. Find the smallest 5-digit number exactly divisible by 21, 28, and 42.
    Answer: 10080
75. Find the smallest 6-digit number exactly divisible by 25, 40, and 50.
    Answer: 100000
76. Find the smallest 4-digit number exactly divisible by 22, 33, and 44.
    Answer: 1056
77. Find the smallest 5-digit number exactly divisible by 24, 36, and 48.
    Answer: 10080
78. Find the smallest 4-digit number exactly divisible by 30, 45, and 60.
    Answer: 1080
79. Find the smallest 5-digit number exactly divisible by 42, 56, and 84.
    Answer: 10080
80. Find the smallest 6-digit number exactly divisible by 48, 64, and 96.
    Answer: 100032
81. Find the smallest 4-digit number exactly divisible by 35, 49, and 70.
    Answer: 1470
82. Find the smallest 5-digit number exactly divisible by 45, 60, and 90.
    Answer: 10080
83. Find the smallest 5-digit number exactly divisible by 72, 90, and 120.
    Answer: 10080
84. Find the smallest 6-digit number exactly divisible by 75, 100, and 150.
    Answer: 100200