Highest common factor HCF and lowest common multiple LCM. - Question Bank

1. The product of two numbers is 960 and their HCF is 10. What is their LCM?
A) 96
B) 10
C) 960
D) Cannot be determined
2. What is the LCM of 1001 and 1010?
A) 1011010
B) 10010010
C) 10110100
D) 10100101
3. What is the HCF of 1001 and 1010?
A) 1
B) 7
C) 11
D) 13
4. Three bells toll at intervals of 12, 15, and 18 minutes respectively. If they start tolling together, after what time will they next toll together?
A) 60 minutes
B) 90 minutes
C) 180 minutes
D) 360 minutes
5. Find the LCM of 144 and 192.
A) 192
B) 384
C) 576
D) 1152
6. Find the HCF of 144 and 192.
A) 12
B) 16
C) 24
D) 48
7. Find the smallest number which when divided by 6, 7, and 8 leaves remainders 3, 4, and 5 respectively.
A) 165
B) 177
C) 189
D) 191
8. The HCF of two numbers is 8. Which of the following cannot be their LCM?
A) 24
B) 48
C) 60
D) 72
9. What is the LCM of 16 and 24?
A) 8
B) 16
C) 24
D) 48
10. What is the HCF of 16 and 24?
A) 4
B) 8
C) 12
D) 16
11. If the HCF of two numbers is 1, the numbers are called:
A) Composite numbers
B) Prime numbers
C) Coprime or relatively prime numbers
D) Even numbers
12. Find the LCM of 108, 120, and 132.
A) 1080
B) 2160
C) 3960
D) 7920
13. Find the HCF of 108, 120, and 132.
A) 6
B) 12
C) 18
D) 36
14. What is the LCM of three numbers a, b, and c?
A) The smallest number that is a multiple of a, b, and c.
B) The largest number that is a multiple of a, b, and c.
C) The product of the common prime factors raised to the lowest power.
D) The product of all prime factors raised to the highest power.
15. What is the HCF of three numbers a, b, and c?
A) The smallest number that divides a, b, and c.
B) The largest number that divides a, b, and c.
C) The product of the common prime factors raised to the lowest power.
D) The product of all prime factors raised to the highest power.
16. Find the LCM of 36 and 84.
A) 12
B) 84
C) 252
D) 504
17. Find the HCF of 36 and 84.
A) 6
B) 12
C) 18
D) 24
18. What is the LCM of 2^3 * 3^2 * 5 and 2^2 * 3^3 * 7?
A) 2^2 * 3^2
B) 2^3 * 3^3
C) 2^2 * 3^3 * 5 * 7
D) 2^3 * 3^3 * 5 * 7
19. What is the HCF of 2^3 * 3^2 * 5 and 2^2 * 3^3 * 7?
A) 2^2 * 3^2
B) 2^3 * 3^3
C) 2^2 * 3^3 * 5 * 7
D) 2^3 * 3^2 * 5 * 7
20. Find the greatest 4-digit number exactly divisible by 6, 8, 12, and 16.
A) 9999
B) 9984
C) 9960
D) 9936
21. Find the smallest 5-digit number exactly divisible by 12, 15, 18, and 20.
A) 10080
B) 10800
C) 11880
D) 12000
22. The HCF of two numbers is 11 and their LCM is 7700. If one number is 275, find the other number.
A) 25
B) 250
C) 308
D) 700
23. Find the LCM of 0.5 and 0.25.
A) 0.125
B) 0.25
C) 0.5
D) 1
24. Find the HCF of 1.2 and 1.8.
A) 0.06
B) 0.6
C) 6
D) 60
25. What is the LCM of 2/3 and 4/5?
A) 8/15
B) 2/5
C) 4/3
D) 10/15
26. What is the HCF of 3/4 and 5/6?
A) 1/12
B) 15/24
C) 1/2
D) 3/2
27. Find the largest number that divides 45, 60, and 75 without leaving a remainder.
A) 3
B) 5
C) 15
D) 30
28. Find the smallest number that is divisible by 25, 30, and 40.
A) 150
B) 300
C) 600
D) 1200
29. The product of two numbers is 4107. If their HCF is 37, find their LCM.
A) 37
B) 111
C) 399
D) 1110
30. What is the HCF of 100, 120, and 140?
A) 10
B) 20
C) 40
D) 60
31. Find the LCM of 15, 25, and 35.
A) 175
B) 525
C) 1050
D) 13125
32. Find the HCF of 54 and 90 using the Euclidean Algorithm.
A) 6
B) 9
C) 18
D) 27
33. If LCM(a, b) = y, then 'y' must be a multiple of:
A) a only
B) b only
C) a and b
D) a or b
34. If HCF(a, b) = x, then 'x' must be a factor of:
A) a only
B) b only
C) a and b
D) a or b
35. What is the LCM of a number and itself?
A) 1
B) 0
C) The number itself
D) Undefined
36. What is the HCF of a number and itself?
A) 1
B) 0
C) The number itself
D) Undefined
37. Find the LCM of 17 and 23 (both are prime numbers).
A) 1
B) 17
C) 23
D) 391
38. Find the HCF of 17 and 23 (both are prime numbers).
A) 1
B) 17
C) 23
D) 391
39. What is the LCM of any two consecutive integers?
A) The product of the two integers
B) The sum of the two integers
C) 1
D) The smaller integer
40. What is the HCF of any two consecutive integers?
A) 0
B) 1
C) 2
D) The smaller integer
41. Find the LCM of 24, 36, and 60.
A) 120
B) 180
C) 360
D) 720
42. Find the HCF of 24, 36, and 60.
A) 4
B) 6
C) 12
D) 24
43. If the HCF of two numbers is 15 and their LCM is 450, and one of the numbers is 75, what is the other number?
A) 30
B) 45
C) 90
D) 150
44. What is the relationship between the HCF and LCM of two positive integers 'a' and 'b'?
A) HCF(a, b) + LCM(a, b) = a * b
B) HCF(a, b) * LCM(a, b) = a + b
C) HCF(a, b) * LCM(a, b) = a * b
D) HCF(a, b) / LCM(a, b) = a * b
45. Using prime factorization, find the LCM of 48 and 60.
A) 12
B) 240
C) 480
D) 600
46. Using prime factorization, find the HCF of 48 and 60.
A) 4
B) 6
C) 12
D) 240
47. If the prime factorization of a number 'a' is p1^x1 * p2^x2 and the prime factorization of a number 'b' is p1^y1 * p2^y2, how is the HCF calculated using prime factorization?
A) p1^(x1+y1) * p2^(x2+y2)
B) p1^(max(x1,y1)) * p2^(max(x2,y2))
C) p1^(min(x1,y1)) * p2^(min(x2,y2))
D) p1^(x1*y1) * p2^(x2*y2)
48. Which method is commonly used to find the HCF of larger numbers by repeatedly applying the division algorithm?
A) Prime Factorization Method
B) Listing Multiples Method
C) Euclidean Algorithm
D) Venn Diagram Method
49. Find the LCM of 12 and 18.
A) 6
B) 18
C) 36
D) 72
50. Find the HCF of 12 and 18.
A) 2
B) 3
C) 6
D) 36
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