Question

Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = Product of the integers.

336 and 54

Answer 1

Given: 336 and 54

Step-wise calculation:

1. Prime factorisation:

336 = 2 × 2 × 2 × 2 × 3 × 7

= 2⁴ × 3 × 7 

And 54 = 2 × 3 × 3 × 3

= 2 × 3³

2. HCF (product of common primes with lowest powers):

Common primes: 2¹ and 3¹ 

⇒ HCF = 2 × 3

⇒ HCF = 6

3. LCM (product of primes with highest powers):

Take 2⁴ (from 336), 3³ (from 54) and 7¹ (from 336):

LCM = 2⁴ × 3³ × 7

= 16 × 27 × 7

= 3024

4. Verify LCM × HCF = product:

LCM × HCF = 3024 × 6 = 18144

336 × 54 = (300 + 36) × 54

= 16200 + 1944

= 18144

HCF = 6, LCM = 3024 and LCM × HCF = 18144 = 336 × 54, so the identity is verified.