Find the LCM of the following

a^{m + 1}, a^{m + 2}, a^{m + 3}

Given terms: –

a^{m + 1}, a^{m + 2}, a^{m + 3}

Formula used: –

LCM = Least Common Multiple

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

divided completely;

a^{m + 1} = a^m × a

a^{m + 2} = a^m × a × a

a^{m + 3} = a^m × a × a × a

⇒ first find the common factors in all terms

Common factor = a^m × a

Common factor from any 2 terms

= ( a^m × a) × [(1)(a)(a²)]

= ( a^m × a) × a[(1)(1)(a)]

⇒ then multiply the remaining factors of terms in common

factor to get the LCM

= ( a^m × a²)(a)

= a^ma³

Conclusion: –

The LCM of given terms [a^{m + 1}, a^{m + 2}, a^{m + 3}] is a^ma³