Question

Identify the least common multiple of:


(x + 1), (x - 1), & (x^2 - 1)

Answer 1

Given:

The expressions are
`(x+1),\ (x-1)` and
`(x^2-1)`.

To find:

The least common multiple of given expressions.

Solution:

The expressions are
`(x+1),\ (x-1)` and
`(x^2-1)`. The factor forms of these expressions are:

`(x+1)=1* (x+1)`

`(x-1)=1* (x-1)`

`(x^2-1)=(x-1)(x+1)`
`[\because a^2-b^2=(a-b)(a+b)]`

The least common multiple is the product of all distinct factors with its highest degree. So,

`L.C.M.=1* (x+1)* (x-1)`

`L.C.M.=(x+1)(x-1)`

`L.C.M.=x^2-1^2`
`[\because a^2-b^2=(a-b)(a+b)]`

`L.C.M.=x^2-1`

Therefore, the least common multiple of given expressions is
`x^2-1`.