Question

Find the HCF and LCM of 12, 15, 18, 27.

Answer 1

Given: 12, 15, 18, 27.

Step-wise calculation:

1. Prime factorise each:

12 = 2² × 3

15 = 3 × 5

18 = 2 × 3²

27 = 3³

2. HCF: Take common primes with smallest exponents:

Only 3 is common; smallest exponent = 1 → HCF = 3¹ = 3.

3. LCM: Take all primes with largest exponents:

2² (from 12), 3³ (from 27), 5¹ (from 15) → LCM = 2² × 3³ × 5

Compute: 4 × 27 × 5

= 108 × 5 

= 540

HCF = 3, LCM = 540.