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

Q1Past 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.
Q2Past 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.
Q3Past 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.
Q4Past 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.
Q5Past 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.
Q6Past 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.
Q7Past 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.
Q8easy
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.
Q9easy
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.
Q10medium
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.
Q11Past 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.
Q12Past 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.
Q13easy
The HCF of 9 and 12 is
1. A1
2. B2
3. C3
4. D4
💡 Explanation:
9 = 3², 12 = 2²×3; common factor = 3.
Q14easy
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.
Q15easy
The HCF of 16 and 24 is
1. A4
2. B8
3. C12
4. D16
💡 Explanation:
16 = 2⁴, 24 = 2³×3; common = 2³ = 8.
Q16medium
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.
Q17easy
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.
Q18easy
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.
Q19easy
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.
Q20Past 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.
Q21Past 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.
Q22easy
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.
Q23medium
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.
Q24Past 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.
Q25medium
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.
Q26medium
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.
Q27medium
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.
Q28medium
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.
Q29easy
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.
Q30easy
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.
Q31easy
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.
Q32easy
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.
Q33easy
The HCF of 12 and 16 is
1. A4
2. B6
3. C8
4. D12
💡 Explanation:
12 = 2²×3, 16 = 2⁴; common = 2² = 4.
Q34medium
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.
Q35medium
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.
Q36Past 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.
Q37Past 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.
Q38easy
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.
Q39medium
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.
Q40medium
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.
Q41easy
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.
Q42Past 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.
Q43medium
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.
Q44hard
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.
Q45easy
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.

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HCF & LCM MCQs 2026

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