HCF and LCM Quiz - ICSE Class 6 Mathematics

Free practice quiz: HCF and LCM (ICSE Class 6 Mathematics). 56 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 6 Mathematics practice quiz has 56 multiple-choice questions on HCF and LCM, and 56 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. Find the Highest Common Factor (HCF) of 24, 36, and 48.

   1. 6
   2. 12
   3. 24
   4. 36
   Show answer

   Answer: B. 12

   To find the HCF, we can list the factors of each number: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 The common factors are 1, 2, 3, 4, 6, and 12. The highest common factor is 12.

2. Find the largest 4-digit number exactly divisible by 12, 18, and 24.

   1. 9972
   2. 9936
   3. 9864
   4. 9900
   Show answer

   Answer: B. 9936

   First, find the LCM of 12, 18, and 24. LCM(12, 18, 24) = 72. Now, find the largest 4-digit number, which is 9999. Divide 9999 by 72: 9999 / 72 = 138 with a remainder of 63. To find the largest multiple of 72 less than or equal to 9999, subtract the remainder from 9999: 9999 - 63 = 9936. Thus, 9936 is the largest 4-digit number divisible by 12, 18, and 24.

3. If the HCF of two numbers is 15 and their LCM is 135. If one number is 45, what is the other number?

   1. 15
   2. 30
   3. 45
   4. 35
   Show answer

   Answer: C. 45

   Using the property: Product of two numbers = HCF x LCM. Let the other number be 'x'. 45 * x = 15 * 135 45x = 2025 x = 2025 / 45 x = 45.

4. Find the largest number that divides 180, 252, and 324 exactly.

   1. 12
   2. 18
   3. 36
   4. 3
   Show answer

   Answer: C. 36

   We need to find the HCF of 180, 252, and 324. Prime factorization: 180 = 2^2 x 3^2 x 5 252 = 2^2 x 3^2 x 7 324 = 2^2 x 3^4 The common prime factors with the lowest powers are 2^2 and 3^2. HCF = 2^2 x 3^2 = 4 x 9 = 36.

5. The product of two numbers is 2000 and their HCF is 10. What is their LCM?

   1. 200
   2. 100
   3. 20
   4. 1000
   Show answer

   Answer: A. 200

   Using the property: Product of two numbers = HCF x LCM. Given: Product = 2000, HCF = 10. So, 2000 = 10 x LCM. LCM = 2000 / 10 = 200.

More questions in this quiz

Answers and explanations are in the full quiz.

1. What is the Least Common Multiple (LCM) of 15, 20, and 25?
2. If the HCF of two numbers is 8 and their product is 576, what is their LCM?
3. Find the HCF of two consecutive even numbers.
4. The LCM of two numbers is 120 and their HCF is 10. If one of the numbers is 30, find the other number.
5. Find the smallest number that is divisible by both 18 and 24.
6. What is the HCF of 75 and 100?
7. Find the LCM of 12, 18, and 30.
8. Find the HCF of 3 prime numbers.
9. The HCF of two numbers is 9 and their LCM is 180. If one of the numbers is 27, find the other number.
10. Which of the following pairs of numbers are coprime?
11. What is the HCF of two consecutive odd numbers?
12. Find the smallest number that leaves a remainder of 5 when divided by 8, 12, and 16.
13. The HCF of two numbers is 16 and their LCM is 192. If one of the numbers is 48, find the other number.
14. The HCF of two numbers is 8. If their LCM is 168, and one of the numbers is 48, find the other number.
15. Find the HCF of 90, 120, and 150.
16. Find the LCM of 42, 56, and 60.
17. Two numbers are in the ratio 3:4 and their HCF is 12. What is their LCM?
18. Find the largest number that divides 201, 268, and 335 exactly.
19. The HCF of two numbers is 18 and their product is 3456. What is their LCM?
20. Find the LCM of 7, 14, and 21.
21. Find the smallest number which when divided by 20, 25, and 30 leaves no remainder.
22. What is the HCF of 64 and 80?
23. The LCM of two numbers is 225 and their HCF is 15. If one of the numbers is 45, find the other number.
24. Find the HCF of 16, 24, and 32.
25. What is the LCM of 18, 27, and 36?
26. The product of two numbers is 4050 and their HCF is 15. What is their LCM?
27. Find the smallest number which when divided by 9, 12, 15, and 18 leaves a remainder of 3 in each case.
28. What is the HCF of 112 and 144?
29. Find the LCM of 1, 2, 3, 4, 5, 6.
30. The HCF of two numbers is 12 and their LCM is 180. If one of the numbers is 36, find the other number.
31. If the HCF of two numbers is 7 and their LCM is 147. If one of the numbers is 21, what is the other number?
32. Find the smallest 5-digit number divisible by 6, 8, and 10.
33. Find the HCF of 30, 45, and 60.
34. The HCF of two numbers is 9 and their LCM is 162. If one of the numbers is 27, find the other number.
35. Find the LCM of 14, 21, and 35.
36. What is the HCF of 84, 120, and 180?
37. The LCM of two numbers is 48 and their HCF is 4. If one of the numbers is 16, find the other number.
38. Find the smallest number that leaves a remainder of 2 when divided by 3, 4, and 5.
39. What is the HCF of 54, 72, and 90?
40. Find the LCM of 8, 12, and 18.
41. Two numbers are in the ratio 5:6 and their HCF is 4. What is their LCM?
42. Find the smallest number that when divided by 7, 14, and 21 leaves a remainder of 4 in each case.
43. If the HCF of two numbers is 14 and their LCM is 196. If one of the numbers is 28, find the other number.
44. What is the HCF of 60, 75, and 90?
45. Find the LCM of 15, 25, and 35.
46. The HCF of two numbers is 18 and their LCM is 216. If one of the numbers is 54, find the other number.
47. Find the largest 4-digit number exactly divisible by 15, 20, 25, and 30.
48. What is the LCM of 5, 7, 10, and 14?
49. The HCF of two numbers is 24. Their LCM is 240. If one number is 48, what is the other number?
50. Find the HCF of 96, 128, and 160.
51. Find the LCM of 12, 15, 18, and 20.

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