Find the LCM of the following

3(a – 1), 2(a – 1)², (a² – 1)

Given terms: –

3(a – 1), 2(a – 1)², (a² – 1)

Formula used: –

LCM = Least Common Multiple

Means it is the lowest term by which every element must be

divided completely;

3(a – 1) = 3 × (a – 1)

2(a – 1)² = 2 × (a – 1) × (a – 1)

(a² – 1) = (a² – 1²) = (a – 1) × (a + 1)

⇒ first find the common factors in all terms

Common factor = (a – 1)

⇒ then multiply the remaining factors of terms in common

factor to get the LCM

= (a – 1) × [(3) × (2(a – 1)) × (a + 1)]

= 6(a + 1)(a – 1)²

Conclusion: –

The LCM of given terms [3(a – 1), 2(a – 1)², (a² – 1)] is

6(a + 1)(a – 1)²