Basic Numeracy (Class X Level) – LCM and HCF

Assam Public Service Commission (APSC)

Combined Competitive Examination (CCE)

Preliminary Examination – General Studies Paper II (Objective Type, 200 Marks)

Topic: Basic Numeracy (Class X Level)

Sub-Topic: LCM and HCF

These questions test your understanding of factors, multiples, Highest Common Factor (HCF), Least Common Multiple (LCM), prime factorization, word problems, and practical applications. Choose the correct answer.

LCM and HCF – MCQs

MCQ 1

The HCF of 12 and 18 is:
A. 2
B. 3
C. 6
D. 12

Correct Answer: C
Explanation:
Common factors: 1, 2, 3, 6 → Highest is 6.

MCQ 2

The LCM of 6 and 8 is:
A. 12
B. 24
C. 36
D. 48

Correct Answer: B
Explanation:
LCM = 2³ × 3 = 24.

MCQ 3

Which of the following is always true?
A. HCF × LCM = Sum of numbers
B. HCF × LCM = Product of numbers
C. HCF = LCM
D. HCF > LCM

Correct Answer: B
Explanation:
For any two numbers,
[
\text{HCF} \times \text{LCM} = \text{Product of the numbers}
]

MCQ 4

The HCF of two numbers is 5 and their LCM is 60. If one number is 15, the other number is:
A. 20
B. 30
C. 25
D. 40

Correct Answer: B
Explanation:
Other number = (HCF × LCM) ÷ given number
= (5 × 60) ÷ 15 = 20 ❌
Correct calculation: 300 ÷ 15 = 20 → option A
✔ Correct Answer: A

MCQ 5

The LCM of two coprime numbers is equal to:
A. Their sum
B. Their difference
C. Their product
D. Their HCF

Correct Answer: C
Explanation:
For coprime numbers, HCF = 1 → LCM = product.

MCQ 6

Which of the following pairs is coprime?
A. 6 and 9
B. 8 and 12
C. 9 and 28
D. 15 and 25

Correct Answer: C
Explanation:
HCF of 9 and 28 = 1.

MCQ 7

The HCF of 24, 36, and 48 is:
A. 6
B. 12
C. 18
D. 24

Correct Answer: B
Explanation:
Common factors → Highest is 12.

MCQ 8

The LCM of 4, 6, and 12 is:
A. 12
B. 18
C. 24
D. 36

Correct Answer: C
Explanation:
LCM = 2³ × 3 = 24.

MCQ 9

Which number is the smallest when divided by 6, 8, and 12 leaves remainder 0?
A. 12
B. 24
C. 36
D. 48

Correct Answer: B
Explanation:
Required number = LCM of 6, 8, 12 = 24.

MCQ 10

The HCF of 45 and 75 is:
A. 5
B. 10
C. 15
D. 25

Correct Answer: C
Explanation:
45 = 3² × 5
75 = 3 × 5²
HCF = 3 × 5 = 15.

MCQ 11

The LCM of 9 and 15 is:
A. 30
B. 45
C. 60
D. 90

Correct Answer: B
Explanation:
LCM = 3² × 5 = 45.

MCQ 12

If HCF of two numbers is 1, the numbers are called:
A. Prime numbers
B. Composite numbers
C. Coprime numbers
D. Even numbers

Correct Answer: C
Explanation:
Numbers with HCF = 1 are coprime.

MCQ 13

The HCF of 72 and 108 is:
A. 18
B. 24
C. 36
D. 54

Correct Answer: C
Explanation:
72 = 2³ × 3²
108 = 2² × 3³
HCF = 2² × 3² = 36.

MCQ 14

The LCM of 10, 15, and 20 is:
A. 30
B. 60
C. 90
D. 120

Correct Answer: B
Explanation:
LCM = 2² × 3 × 5 = 60.

MCQ 15

Two numbers have HCF 12 and LCM 180. If one number is 36, the other number is:
A. 48
B. 60
C. 72
D. 90

Correct Answer: B
Explanation:
Other number = (12 × 180) ÷ 36 = 60.

MCQ 16

The HCF of two consecutive natural numbers is always:
A. 0
B. 1
C. 2
D. The smaller number

Correct Answer: B
Explanation:
Consecutive numbers are always coprime.

MCQ 17

Which of the following numbers has maximum HCF with 24?
A. 18
B. 36
C. 48
D. 50

Correct Answer: C
Explanation:
HCF(24, 48) = 24 (maximum).

MCQ 18

The LCM of two numbers is 240 and their HCF is 10. If one number is 40, the other number is:
A. 50
B. 60
C. 80
D. 90

Correct Answer: B
Explanation:
Other number = (10 × 240) ÷ 40 = 60.

MCQ 19

Which method is commonly used to find HCF of large numbers?
A. Division method
B. Multiplication method
C. Subtraction method
D. Average method

Correct Answer: A
Explanation:
The Euclid division method is efficient.

MCQ 20

The HCF of 1 and any natural number is:
A. 0
B. 1
C. The number itself
D. Cannot be determined

Correct Answer: B
Explanation:
1 is a factor of every number.

MCQ 21

Which of the following numbers is divisible by both 6 and 9?
A. 18
B. 27
C. 36
D. 45

Correct Answer: C
Explanation:
LCM of 6 and 9 = 18 → 36 is a multiple.

MCQ 22

The HCF of three numbers is 1. The numbers are necessarily:
A. Prime
B. Composite
C. Coprime
D. Even

Correct Answer: C
Explanation:
HCF = 1 indicates coprime relation.

MCQ 23

The smallest number which is exactly divisible by 8, 12, and 15 is:
A. 120
B. 180
C. 240
D. 360

Correct Answer: C
Explanation:
LCM of 8, 12, 15 = 240.

MCQ 24

If the HCF of two numbers is 8 and their product is 1,536, the LCM is:
A. 96
B. 128
C. 192
D. 256

Correct Answer: C
Explanation:
LCM = 1536 ÷ 8 = 192.

MCQ 25

The HCF of 0 and 15 is:
A. 0
B. 1
C. 15
D. Undefined

Correct Answer: C
Explanation:
HCF(0, n) = n.

MCQ 26

The LCM of two prime numbers is always:
A. Their sum
B. Their difference
C. Their product
D. Their HCF

Correct Answer: C
Explanation:
Prime numbers have no common factors except 1.

MCQ 27

Which of the following is not a factor of 36?
A. 3
B. 6
C. 9
D. 11

Correct Answer: D
Explanation:
11 does not divide 36.

MCQ 28

The HCF of 84 and 126 is:
A. 14
B. 21
C. 28
D. 42

Correct Answer: B
Explanation:
84 = 2² × 3 × 7
126 = 2 × 3² × 7
HCF = 2 × 3 × 7 = 21.

MCQ 29

The LCM of 5, 10, and 20 is:
A. 10
B. 20
C. 40
D. 50

Correct Answer: B
Explanation:
LCM = 20.

MCQ 30

LCM and HCF questions mainly test:
A. Memorization
B. Approximation
C. Logical understanding of number properties
D. Language ability

Correct Answer: C
Explanation:
They assess divisibility, factorization, and numerical reasoning skills.

✅ APSC Exam Relevance

These MCQs comprehensively cover factorization, HCF–LCM relations, word problems, and real-life applications, strictly aligned with APSC CCE GS Paper II – Basic Numeracy (Class X level).

• LCM and HCF questions for competitive exams

• Basic numeracy LCM HCF MCQs GS Paper II

• Divisibility and factorization questions APSC

• LCM HCF word problems with answers

• Class X level LCM and HCF practice