HCF & LCM MCQs 2026

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

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Page 1 of 1Questions 1–10 of 45

Q1medium
The HCF of 36 and 48 is
1. A6
2. B12
3. C18
4. D24
💡 Explanation:
36 = 2²×3², 48 = 2⁴×3; common = 2²×3 = 12.
Q2Past Paper · PPSC/FPSC/NTSmedium
The product of two numbers is 96 and their HCF is 4. Their LCM is
1. A4
2. B12
3. C16
4. D24
💡 Explanation:
LCM = product ÷ HCF = 96 ÷ 4 = 24.
Q3medium
The HCF of two numbers is a ______ of their LCM
1. AMultiple
2. BFactor
3. CSum
4. DSquare
💡 Explanation:
The HCF always divides the LCM, so it is a factor of the LCM.
Q4hard
The LCM of 36 and 48 is
1. A72
2. B96
3. C120
4. D144
💡 Explanation:
36 = 2²×3², 48 = 2⁴×3; LCM = 2⁴×3² = 144.
Q5Past Paper · PPSC/FPSC/NTShard
Two numbers have HCF 6 and LCM 36. If one number is 12, the other is
1. A18
2. B24
3. C30
4. D6
💡 Explanation:
Product = HCF×LCM = 6×36 = 216; other number = 216 ÷ 12 = 18.
Q6easy
The HCF of 14 and 21 is
1. A3
2. B5
3. C7
4. D14
💡 Explanation:
14 = 2×7, 21 = 3×7; common factor = 7.
Q7medium
The LCM of 14 and 21 is
1. A21
2. B42
3. C63
4. D84
💡 Explanation:
14 = 2×7, 21 = 3×7; LCM = 2×3×7 = 42.
Q8medium
The greatest number that divides both 24 and 36 exactly is
1. A4
2. B6
3. C8
4. D12
💡 Explanation:
The HCF of 24 and 36 is 12, the greatest number dividing both.
Q9easy
The HCF of 5 and 7 is
1. A5
2. B7
3. C35
4. D1
💡 Explanation:
5 and 7 are both prime and co-prime, so their HCF is 1.
Q10easy
The smallest number that is a common multiple of 4 and 5 is
1. A20
2. B9
3. C40
4. D10
💡 Explanation:
4 and 5 are co-prime, so their smallest common multiple (LCM) is 20.
Q11Past Paper · PPSC/FPSC/NTSmedium
For any two numbers, HCF × LCM equals
1. AHCF + LCM
2. BSum of the numbers
3. CProduct of the numbers
4. DDifference of the numbers
💡 Explanation:
HCF × LCM of two numbers always equals the product of those numbers.
Q12easy
The HCF of 25 and 30 is
1. A1
2. B3
3. C5
4. D10
💡 Explanation:
25 = 5², 30 = 2×3×5; common factor = 5.
Q13Past Paper · PPSC/FPSC/NTSeasy
The HCF of 8 and 12 is
1. A2
2. B4
3. C6
4. D8
💡 Explanation:
8 = 2³, 12 = 2²×3; common factor = 2² = 4.
Q14easy
The LCM of 8 and 12 is
1. A12
2. B16
3. C20
4. D24
💡 Explanation:
8 = 2³, 12 = 2²×3; LCM = 2³×3 = 24.
Q15easy
The HCF of 15 and 20 is
1. A2
2. B3
3. C5
4. D10
💡 Explanation:
15 = 3×5, 20 = 2²×5; common factor = 5.
Q16medium
The LCM of 15 and 20 is
1. A60
2. B40
3. C30
4. D120
💡 Explanation:
15 = 3×5, 20 = 2²×5; LCM = 2²×3×5 = 60.
Q17Past Paper · PPSC/FPSC/NTSmedium
The HCF of two co-prime numbers is always
1. A0
2. B1
3. C2
4. DTheir product
💡 Explanation:
Co-prime numbers share no common factor except 1, so their HCF is 1.
Q18Past Paper · PPSC/FPSC/NTSmedium
The LCM of two co-prime numbers is equal to
1. A1
2. BTheir HCF
3. CTheir sum
4. DTheir product
💡 Explanation:
For co-prime numbers, the LCM equals the product of the two numbers.
Q19easy
The HCF of 9 and 12 is
1. A1
2. B2
3. C3
4. D4
💡 Explanation:
9 = 3², 12 = 2²×3; common factor = 3.
Q20easy
The LCM of 4 and 6 is
1. A12
2. B6
3. C10
4. D24
💡 Explanation:
4 = 2², 6 = 2×3; LCM = 2²×3 = 12.
Q21easy
The HCF of 16 and 24 is
1. A4
2. B8
3. C12
4. D16
💡 Explanation:
16 = 2⁴, 24 = 2³×3; common = 2³ = 8.
Q22medium
The LCM of 16 and 24 is
1. A24
2. B32
3. C40
4. D48
💡 Explanation:
16 = 2⁴, 24 = 2³×3; LCM = 2⁴×3 = 48.
Q23easy
The LCM of 3 and 5 is
1. A8
2. B5
3. C15
4. D30
💡 Explanation:
3 and 5 are co-prime, so LCM = 3×5 = 15.
Q24easy
The HCF of 7 and 14 is
1. A7
2. B1
3. C2
4. D14
💡 Explanation:
7 divides both 7 and 14, so the HCF is 7.
Q25easy
The LCM of 7 and 14 is
1. A7
2. B14
3. C21
4. D28
💡 Explanation:
14 is a multiple of 7, so the LCM of 7 and 14 is 14.
Q26Past Paper · PPSC/FPSC/NTSmedium
For two numbers a and b, HCF × LCM equals
1. Aa + b
2. Ba − b
3. CHCF + LCM
4. Da × b
💡 Explanation:
The product of the HCF and LCM of two numbers equals the product of the numbers.
Q27Past Paper · PPSC/FPSC/NTSmedium
For the numbers 12 and 18, the product of their HCF and LCM is
1. A30
2. B108
3. C216
4. D200
💡 Explanation:
HCF = 6 and LCM = 36, so 6×36 = 216, which also equals 12×18.
Q28easy
The HCF of 20 and 30 is
1. A10
2. B5
3. C15
4. D20
💡 Explanation:
20 = 2²×5, 30 = 2×3×5; common = 2×5 = 10.
Q29medium
The LCM of 20 and 30 is
1. A50
2. B60
3. C90
4. D120
💡 Explanation:
20 = 2²×5, 30 = 2×3×5; LCM = 2²×3×5 = 60.
Q30Past Paper · PPSC/FPSC/NTSmedium
The smallest number exactly divisible by 2, 3, 4, 5 and 6 is
1. A30
2. B45
3. C50
4. D60
💡 Explanation:
The LCM of 2, 3, 4, 5 and 6 is 60, the smallest number divisible by all.
Q31medium
The HCF of 18, 24 and 30 is
1. A2
2. B3
3. C6
4. D12
💡 Explanation:
18 = 2×3², 24 = 2³×3, 30 = 2×3×5; common = 2×3 = 6.
Q32medium
The LCM of 5, 10 and 15 is
1. A30
2. B45
3. C60
4. D15
💡 Explanation:
5, 10 = 2×5, 15 = 3×5; LCM = 2×3×5 = 30.
Q33medium
The HCF of two numbers is always
1. AGreater than both numbers
2. BA factor of both numbers
3. CEqual to their sum
4. DA multiple of both
💡 Explanation:
The HCF is a common factor and therefore divides both numbers.
Q34medium
The LCM of two numbers is always
1. ALess than both
2. BEqual to their HCF
3. CA factor of both
4. DA multiple of both
💡 Explanation:
The LCM is a common multiple, so it is a multiple of both numbers.
Q35medium
The LCM of 12 and 16 is
1. A24
2. B36
3. C48
4. D96
💡 Explanation:
12 = 2²×3, 16 = 2⁴; LCM = 2⁴×3 = 48.
Q36easy
The LCM of 6 and 8 is
1. A24
2. B12
3. C16
4. D48
💡 Explanation:
6 = 2×3, 8 = 2³; LCM = 2³×3 = 24.
Q37easy
The HCF of 10 and 15 is
1. A3
2. B5
3. C10
4. D15
💡 Explanation:
10 = 2×5, 15 = 3×5; common factor = 5.
Q38easy
The LCM of 10 and 15 is
1. A15
2. B20
3. C25
4. D30
💡 Explanation:
10 = 2×5, 15 = 3×5; LCM = 2×3×5 = 30.
Q39easy
The HCF of 12 and 16 is
1. A4
2. B6
3. C8
4. D12
💡 Explanation:
12 = 2²×3, 16 = 2⁴; common = 2² = 4.
Q40Past Paper · PPSC/FPSC/NTSeasy
HCF stands for
1. AHighest Common Fraction
2. BHigh Common Factor
3. CHighest Common Factor
4. DHigher Common Function
💡 Explanation:
HCF stands for Highest Common Factor, the largest number that divides given numbers.
Q41Past Paper · PPSC/FPSC/NTSeasy
LCM stands for
1. ALeast Common Multiple
2. BLowest Common Measure
3. CLargest Common Multiple
4. DLeast Common Measure
💡 Explanation:
LCM stands for Least Common Multiple, the smallest common multiple of given numbers.
Q42Past Paper · PPSC/FPSC/NTSeasy
The HCF of 12 and 18 is
1. A3
2. B6
3. C9
4. D12
💡 Explanation:
12 = 2²×3 and 18 = 2×3²; the common factors give HCF = 2×3 = 6.
Q43Past Paper · PPSC/FPSC/NTSeasy
The LCM of 12 and 18 is
1. A6
2. B18
3. C24
4. D36
💡 Explanation:
12 = 2²×3, 18 = 2×3²; LCM takes highest powers = 2²×3² = 36.
Q44Past Paper · PPSC/FPSC/NTSeasy
The HCF of 24 and 36 is
1. A6
2. B8
3. C12
4. D18
💡 Explanation:
24 = 2³×3, 36 = 2²×3²; common = 2²×3 = 12.
Q45Past Paper · PPSC/FPSC/NTSmedium
The LCM of 24 and 36 is
1. A72
2. B36
3. C60
4. D96
💡 Explanation:
24 = 2³×3, 36 = 2²×3²; LCM = 2³×3² = 72.

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HCF & LCM MCQs 2026

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