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HCF & LCM MCQs 2026

45 questions with detailed answers · 15 from past papers · 5 quiz batches available

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Read each question, think about the answer, then click Show Answer to reveal the correct option and explanation. Load 10 at a time so it stays manageable — perfect for one-topic study sessions on the bus or during a break.

Page 1 of 1 Questions 1–10 of 45
  1. Q1 medium

    The LCM of 12 and 16 is

    1. A 24
    2. B 36
    3. C 48
    4. D 96
    💡 Explanation:

    12 = 2²×3, 16 = 2⁴; LCM = 2⁴×3 = 48.

  2. Q2 Past Paper · PPSC/FPSC/NTS easy

    HCF stands for

    1. A Highest Common Fraction
    2. B High Common Factor
    3. C Highest Common Factor
    4. D Higher Common Function
    💡 Explanation:

    HCF stands for Highest Common Factor, the largest number that divides given numbers.

  3. Q3 Past Paper · PPSC/FPSC/NTS easy

    LCM stands for

    1. A Least Common Multiple
    2. B Lowest Common Measure
    3. C Largest Common Multiple
    4. D Least Common Measure
    💡 Explanation:

    LCM stands for Least Common Multiple, the smallest common multiple of given numbers.

  4. Q4 Past Paper · PPSC/FPSC/NTS easy

    The HCF of 12 and 18 is

    1. A 3
    2. B 6
    3. C 9
    4. D 12
    💡 Explanation:

    12 = 2²×3 and 18 = 2×3²; the common factors give HCF = 2×3 = 6.

  5. Q5 Past Paper · PPSC/FPSC/NTS easy

    The LCM of 12 and 18 is

    1. A 6
    2. B 18
    3. C 24
    4. D 36
    💡 Explanation:

    12 = 2²×3, 18 = 2×3²; LCM takes highest powers = 2²×3² = 36.

  6. Q6 Past Paper · PPSC/FPSC/NTS easy

    The HCF of 24 and 36 is

    1. A 6
    2. B 8
    3. C 12
    4. D 18
    💡 Explanation:

    24 = 2³×3, 36 = 2²×3²; common = 2²×3 = 12.

  7. Q7 Past Paper · PPSC/FPSC/NTS medium

    The LCM of 24 and 36 is

    1. A 72
    2. B 36
    3. C 60
    4. D 96
    💡 Explanation:

    24 = 2³×3, 36 = 2²×3²; LCM = 2³×3² = 72.

  8. Q8 Past Paper · PPSC/FPSC/NTS easy

    The HCF of 8 and 12 is

    1. A 2
    2. B 4
    3. C 6
    4. D 8
    💡 Explanation:

    8 = 2³, 12 = 2²×3; common factor = 2² = 4.

  9. Q9 easy

    The LCM of 8 and 12 is

    1. A 12
    2. B 16
    3. C 20
    4. D 24
    💡 Explanation:

    8 = 2³, 12 = 2²×3; LCM = 2³×3 = 24.

  10. Q10 easy

    The HCF of 15 and 20 is

    1. A 2
    2. B 3
    3. C 5
    4. D 10
    💡 Explanation:

    15 = 3×5, 20 = 2²×5; common factor = 5.

  11. Q11 medium

    The LCM of 15 and 20 is

    1. A 60
    2. B 40
    3. C 30
    4. D 120
    💡 Explanation:

    15 = 3×5, 20 = 2²×5; LCM = 2²×3×5 = 60.

  12. Q12 Past Paper · PPSC/FPSC/NTS medium

    The HCF of two co-prime numbers is always

    1. A 0
    2. B 1
    3. C 2
    4. D Their product
    💡 Explanation:

    Co-prime numbers share no common factor except 1, so their HCF is 1.

  13. Q13 Past Paper · PPSC/FPSC/NTS medium

    The LCM of two co-prime numbers is equal to

    1. A 1
    2. B Their HCF
    3. C Their sum
    4. D Their product
    💡 Explanation:

    For co-prime numbers, the LCM equals the product of the two numbers.

  14. Q14 easy

    The HCF of 9 and 12 is

    1. A 1
    2. B 2
    3. C 3
    4. D 4
    💡 Explanation:

    9 = 3², 12 = 2²×3; common factor = 3.

  15. Q15 easy

    The LCM of 4 and 6 is

    1. A 12
    2. B 6
    3. C 10
    4. D 24
    💡 Explanation:

    4 = 2², 6 = 2×3; LCM = 2²×3 = 12.

  16. Q16 easy

    The HCF of 16 and 24 is

    1. A 4
    2. B 8
    3. C 12
    4. D 16
    💡 Explanation:

    16 = 2⁴, 24 = 2³×3; common = 2³ = 8.

  17. Q17 medium

    The LCM of 16 and 24 is

    1. A 24
    2. B 32
    3. C 40
    4. D 48
    💡 Explanation:

    16 = 2⁴, 24 = 2³×3; LCM = 2⁴×3 = 48.

  18. Q18 easy

    The LCM of 3 and 5 is

    1. A 8
    2. B 5
    3. C 15
    4. D 30
    💡 Explanation:

    3 and 5 are co-prime, so LCM = 3×5 = 15.

  19. Q19 easy

    The HCF of 7 and 14 is

    1. A 7
    2. B 1
    3. C 2
    4. D 14
    💡 Explanation:

    7 divides both 7 and 14, so the HCF is 7.

  20. Q20 easy

    The LCM of 7 and 14 is

    1. A 7
    2. B 14
    3. C 21
    4. D 28
    💡 Explanation:

    14 is a multiple of 7, so the LCM of 7 and 14 is 14.

  21. Q21 Past Paper · PPSC/FPSC/NTS medium

    For two numbers a and b, HCF × LCM equals

    1. A a + b
    2. B a − b
    3. C HCF + LCM
    4. D a × b
    💡 Explanation:

    The product of the HCF and LCM of two numbers equals the product of the numbers.

  22. Q22 Past Paper · PPSC/FPSC/NTS medium

    For the numbers 12 and 18, the product of their HCF and LCM is

    1. A 30
    2. B 108
    3. C 216
    4. D 200
    💡 Explanation:

    HCF = 6 and LCM = 36, so 6×36 = 216, which also equals 12×18.

  23. Q23 easy

    The HCF of 20 and 30 is

    1. A 10
    2. B 5
    3. C 15
    4. D 20
    💡 Explanation:

    20 = 2²×5, 30 = 2×3×5; common = 2×5 = 10.

  24. Q24 medium

    The LCM of 20 and 30 is

    1. A 50
    2. B 60
    3. C 90
    4. D 120
    💡 Explanation:

    20 = 2²×5, 30 = 2×3×5; LCM = 2²×3×5 = 60.

  25. Q25 Past Paper · PPSC/FPSC/NTS medium

    The smallest number exactly divisible by 2, 3, 4, 5 and 6 is

    1. A 30
    2. B 45
    3. C 50
    4. D 60
    💡 Explanation:

    The LCM of 2, 3, 4, 5 and 6 is 60, the smallest number divisible by all.

  26. Q26 medium

    The HCF of 18, 24 and 30 is

    1. A 2
    2. B 3
    3. C 6
    4. D 12
    💡 Explanation:

    18 = 2×3², 24 = 2³×3, 30 = 2×3×5; common = 2×3 = 6.

  27. Q27 medium

    The LCM of 5, 10 and 15 is

    1. A 30
    2. B 45
    3. C 60
    4. D 15
    💡 Explanation:

    5, 10 = 2×5, 15 = 3×5; LCM = 2×3×5 = 30.

  28. Q28 medium

    The HCF of two numbers is always

    1. A Greater than both numbers
    2. B A factor of both numbers
    3. C Equal to their sum
    4. D A multiple of both
    💡 Explanation:

    The HCF is a common factor and therefore divides both numbers.

  29. Q29 medium

    The LCM of two numbers is always

    1. A Less than both
    2. B Equal to their HCF
    3. C A factor of both
    4. D A multiple of both
    💡 Explanation:

    The LCM is a common multiple, so it is a multiple of both numbers.

  30. Q30 easy

    The HCF of 25 and 30 is

    1. A 1
    2. B 3
    3. C 5
    4. D 10
    💡 Explanation:

    25 = 5², 30 = 2×3×5; common factor = 5.

  31. Q31 easy

    The LCM of 6 and 8 is

    1. A 24
    2. B 12
    3. C 16
    4. D 48
    💡 Explanation:

    6 = 2×3, 8 = 2³; LCM = 2³×3 = 24.

  32. Q32 easy

    The HCF of 10 and 15 is

    1. A 3
    2. B 5
    3. C 10
    4. D 15
    💡 Explanation:

    10 = 2×5, 15 = 3×5; common factor = 5.

  33. Q33 easy

    The LCM of 10 and 15 is

    1. A 15
    2. B 20
    3. C 25
    4. D 30
    💡 Explanation:

    10 = 2×5, 15 = 3×5; LCM = 2×3×5 = 30.

  34. Q34 easy

    The HCF of 12 and 16 is

    1. A 4
    2. B 6
    3. C 8
    4. D 12
    💡 Explanation:

    12 = 2²×3, 16 = 2⁴; common = 2² = 4.

  35. Q35 Past Paper · PPSC/FPSC/NTS medium

    For any two numbers, HCF × LCM equals

    1. A HCF + LCM
    2. B Sum of the numbers
    3. C Product of the numbers
    4. D Difference of the numbers
    💡 Explanation:

    HCF × LCM of two numbers always equals the product of those numbers.

  36. Q36 easy

    The HCF of 14 and 21 is

    1. A 3
    2. B 5
    3. C 7
    4. D 14
    💡 Explanation:

    14 = 2×7, 21 = 3×7; common factor = 7.

  37. Q37 medium

    The HCF of 36 and 48 is

    1. A 6
    2. B 12
    3. C 18
    4. D 24
    💡 Explanation:

    36 = 2²×3², 48 = 2⁴×3; common = 2²×3 = 12.

  38. Q38 hard

    The LCM of 36 and 48 is

    1. A 72
    2. B 96
    3. C 120
    4. D 144
    💡 Explanation:

    36 = 2²×3², 48 = 2⁴×3; LCM = 2⁴×3² = 144.

  39. Q39 Past Paper · PPSC/FPSC/NTS hard

    Two numbers have HCF 6 and LCM 36. If one number is 12, the other is

    1. A 18
    2. B 24
    3. C 30
    4. D 6
    💡 Explanation:

    Product = HCF×LCM = 6×36 = 216; other number = 216 ÷ 12 = 18.

  40. Q40 easy

    The HCF of 5 and 7 is

    1. A 5
    2. B 7
    3. C 35
    4. D 1
    💡 Explanation:

    5 and 7 are both prime and co-prime, so their HCF is 1.

  41. Q41 Past Paper · PPSC/FPSC/NTS medium

    The product of two numbers is 96 and their HCF is 4. Their LCM is

    1. A 4
    2. B 12
    3. C 16
    4. D 24
    💡 Explanation:

    LCM = product ÷ HCF = 96 ÷ 4 = 24.

  42. Q42 medium

    The LCM of 14 and 21 is

    1. A 21
    2. B 42
    3. C 63
    4. D 84
    💡 Explanation:

    14 = 2×7, 21 = 3×7; LCM = 2×3×7 = 42.

  43. Q43 medium

    The HCF of two numbers is a ______ of their LCM

    1. A Multiple
    2. B Factor
    3. C Sum
    4. D Square
    💡 Explanation:

    The HCF always divides the LCM, so it is a factor of the LCM.

  44. Q44 medium

    The greatest number that divides both 24 and 36 exactly is

    1. A 4
    2. B 6
    3. C 8
    4. D 12
    💡 Explanation:

    The HCF of 24 and 36 is 12, the greatest number dividing both.

  45. Q45 easy

    The smallest number that is a common multiple of 4 and 5 is

    1. A 20
    2. B 9
    3. C 40
    4. D 10
    💡 Explanation:

    4 and 5 are co-prime, so their smallest common multiple (LCM) is 20.

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