Q. 75.0( 2 Votes )

# Find the LCM of the following

3(a – 1), 2(a – 1)^{2}, (a^{2} – 1)

Answer :

__Given terms__: –

3(a – 1), 2(a – 1)^{2}, (a^{2} – 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)

(a^{2} – 1) = (a^{2} – 1^{2}) = (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}, (a^{2} – 1)] is

__6(a + 1)(a – 1) ^{2}__

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