SSC CHSL 2027: LCM and HCF Questions Using Prime Factorisation

LCM and HCF are important topics in quantitative aptitude for SSC CHSL 2027 preparation. The prime factorisation method makes these questions easier to solve accurately. In this quick revision guide, learn the basic rules, follow solved examples and practise exam-style questions.

1. What Are LCM and HCF?

HCF (Highest Common Factor): The greatest number that divides all the given numbers exactly.

LCM (Least Common Multiple): The smallest positive number that is exactly divisible by all the given numbers.

2. Prime Factorisation Method

Prime factorisation means expressing a number as a product of prime numbers.

• For HCF: Multiply only the common prime factors, using the smallest power of each.
• For LCM: Multiply all prime factors present, using the greatest power of each.

3. Solved Examples

Example 1: Find the HCF of 24 and 36.

Prime factorisation:

24 = 2³ × 3

36 = 2² × 3²

Common prime factors with the smallest powers are 2² and 3.

HCF = 2² × 3 = 12

Example 2: Find the LCM of 12 and 18.

Prime factorisation:

12 = 2² × 3

18 = 2 × 3²

Take the greatest power of each prime factor.

LCM = 2² × 3² = 36

Quick visual revision: For 12 and 18, the first common positive multiple is 36.

4. Important Formula

For two positive integers:

HCF × LCM = Product of the two numbers

Example: For 12 and 18:

HCF = 6 and LCM = 36

HCF × LCM = 6 × 36 = 216

Product = 12 × 18 = 216

5. SSC CHSL 2027 Practice Questions

1. Find the HCF of 18 and 30.
A. 3
B. 6
C. 9
D. 12
Answer: B. 6

2. Find the LCM of 8 and 12.
A. 16
B. 20
C. 24
D. 36
Answer: C. 24

3. The prime factorisation of 20 is:
A. 2 × 10
B. 2² × 5
C. 4 × 5
D. 2 × 5
Answer: B. 2² × 5

4. Find the HCF of 16 and 24.
A. 4
B. 6
C. 8
D. 12
Answer: C. 8

5. Find the LCM of 15 and 20.
A. 30
B. 45
C. 50
D. 60
Answer: D. 60

6. Frequently Asked Questions

Conclusion

For SSC CHSL 2027, practise finding common prime factors for HCF and the highest powers of prime factors for LCM. Regular practice will help improve calculation speed and accuracy.