LCM and HCF - Question Bank

1. Find the LCM of $2^3 imes 3^2 imes 5$ and $2^2 imes 3^3 imes 7$.
A) $2^3 imes 3^3 imes 5 imes 7$
B) $2^2 imes 3^2$
C) $2^3 imes 3^2 imes 5$
D) $2^2 imes 3^3 imes 7$
2. Find the HCF of $2^3 imes 3^2 imes 5$ and $2^2 imes 3^3 imes 7$.
A) $2^2 imes 3^2$
B) $2^3 imes 3^3$
C) $2^2 imes 3^2 imes 5 imes 7$
D) $2 imes 3$
3. What is the least number which when divided by 18, 24, and 32 leaves remainders 5, 11, and 19 respectively?
A) 216
B) 221
C) 432
D) 441
4. Find the greatest common divisor of 513 and 693.
A) 3
B) 9
C) 27
D) 81
5. The HCF of two numbers is 9 and their LCM is 135. If one of the numbers is 27, find the other number.
A) 9
B) 18
C) 45
D) 135
6. What is the LCM of 0.6 and 0.8?
A) 0.048
B) 0.48
C) 2.4
D) 4.8
7. What is the HCF of 1.5 and 0.75?
A) 0.25
B) 0.5
C) 0.75
D) 1.5
8. Find the LCM of 135 and 225.
A) 135
B) 225
C) 405
D) 675
9. Find the HCF of 135 and 225.
A) 15
B) 30
C) 45
D) 60
10. What is the smallest number that is divisible by all integers from 1 to 10?
A) 2520
B) 5040
C) 1010
D) 3628800
11. The product of two numbers is 1200 and their HCF is 10. What is their LCM?
A) 12
B) 120
C) 1200
D) 12000
12. Find the HCF of 72, 108, and 180.
A) 12
B) 18
C) 36
D) 72
13. Find the LCM of 16, 20, and 24.
A) 80
B) 120
C) 240
D) 480
14. If HCF(a, b) = 6 and LCM(a, b) = 36, and one number is 12, what is the other number?
A) 6
B) 18
C) 24
D) 36
15. What is the LCM of 30 and 45?
A) 60
B) 90
C) 135
D) 180
16. What is the HCF of 36 and 48?
A) 6
B) 8
C) 12
D) 24
17. Find the largest 5-digit number that is exactly divisible by 3, 4, 5, and 6.
A) 99960
B) 99980
C) 99990
D) 100000
18. Find the smallest number that leaves a remainder of 1 when divided by 2, 3, 4, 5, and 6.
A) 59
B) 60
C) 61
D) 121
19. The HCF of two numbers is 8. If the numbers are 8x and 8y where x and y are coprime, find their LCM in terms of x and y.
A) 8
B) 8xy
C) 64xy
D) x+y
20. Three numbers are in the ratio 2:3:4 and their HCF is 12. Find the numbers.
A) 12, 18, 24
B) 24, 36, 48
C) 36, 54, 72
D) 48, 72, 96
21. Find the HCF of 1.5, 2.5, and 3.5.
A) 0.1
B) 0.5
C) 1
D) 1.5
22. Find the LCM of 5/6, 7/8, and 9/10.
A) 315/40
B) 315/2
C) 315/4
D) 630/1
23. If HCF(a, b) = 12 and a * b = 1800, find LCM(a, b).
A) 12
B) 150
C) 180
D) 1812
24. What is the LCM of 24, 36, and 40?
A) 120
B) 240
C) 360
D) 720
25. What is the HCF of 96 and 120?
A) 12
B) 16
C) 24
D) 32
26. Find the smallest number which when divided by 6, 7, and 8 leaves remainders 3, 4, and 5 respectively.
A) 165
B) 171
C) 183
D) 195
27. The LCM of three numbers is 120. Which of the following cannot be their HCF?
A) 1
B) 10
C) 12
D) 15
28. Find the HCF of 108 and 144 using the Euclidean algorithm.
A) 12
B) 18
C) 24
D) 36
29. What is the HCF of $2^4 imes 3^3 imes 5^2$ and $2^3 imes 3^5 imes 7$?
A) $2^4 imes 3^5 imes 5^2 imes 7$
B) $2^3 imes 3^3 imes 5^2$
C) $2^3 imes 3^3$
D) $2^4 imes 3^3 imes 5^2$
30. What is the LCM of $2^3 imes 3^2 imes 5$ and $2^2 imes 3^3 imes 7$?
A) $2^3 imes 3^3 imes 5 imes 7$
B) $2^2 imes 3^2 imes 5 imes 7$
C) $2^3 imes 3^2 imes 5$
D) $2^2 imes 3^3 imes 7$
31. Find the greatest number that divides 122 and 243 leaving remainders 2 and 3 respectively.
A) 10
B) 12
C) 20
D) 30
32. Two bells toll at intervals of 12 minutes and 15 minutes respectively. If they both start tolling together, after how much time will they next toll together?
A) 3 minutes
B) 12 minutes
C) 60 minutes
D) 180 minutes
33. Find the LCM of 1.2 and 0.4.
A) 0.4
B) 1.2
C) 2.4
D) 4.8
34. Find the HCF of 0.5 and 0.25.
A) 0.1
B) 0.25
C) 0.5
D) 1
35. What is the HCF of 3/4 and 6/7?
A) 3/28
B) 9/28
C) 1/28
D) 18/7
36. What is the LCM of 2/3 and 4/5?
A) 2/15
B) 4/15
C) 8/15
D) 4/5
37. Find the largest 3-digit number which is exactly divisible by 15, 20, and 30.
A) 900
B) 930
C) 960
D) 990
38. Find the smallest 4-digit number which is exactly divisible by 12, 18, and 24.
A) 1008
B) 1080
C) 1152
D) 1296
39. The HCF of two numbers is 16 and their LCM is 384. If one of the numbers is 64, find the other number.
A) 16
B) 48
C) 96
D) 128
40. What is the LCM of 15, 20, and 25?
A) 100
B) 150
C) 200
D) 300
41. What is the HCF of 18, 27, and 45?
A) 3
B) 6
C) 9
D) 18
42. If the LCM of two numbers is 60 and their HCF is 5, and one of the numbers is 20, what is the other number?
A) 10
B) 15
C) 25
D) 30
43. Find the HCF of 100 and 120.
A) 10
B) 20
C) 40
D) 60
44. Find the LCM of 7, 14, and 21.
A) 7
B) 14
C) 21
D) 42
45. What is the largest number that divides 30 and 42 without leaving a remainder?
A) 2
B) 3
C) 6
D) 12
46. What is the smallest number that is divisible by both 6 and 9?
A) 3
B) 6
C) 9
D) 18
47. The product of two numbers is 400 and their HCF is 5. What is their LCM?
A) 20
B) 80
C) 2000
D) 405
48. Find the HCF of 15, 25, and 35.
A) 1
B) 3
C) 5
D) 15
49. Find the LCM of 4, 6, and 8.
A) 12
B) 24
C) 48
D) 96
50. What is the Highest Common Factor (HCF) of 24 and 36?
A) 4
B) 6
C) 12
D) 24
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