Question

How do you find the LCM for `x^2+2x-8` and `x+4`?

Answer 1

`x^2+2x-8` is the Least Common Multiple

Explanation:

Since `x+4` is a factor of `x^2+2x-8`
`color(white)("XXXX")` `color(white)("XXXX")`(`x^2+2x-8 = (x+4)(x-2)`)
and since the LCM of any term can not be less than either of the terms (that is, in this case it can not be less than `(x^2+2x-8)`)

`x^2+2x-8`
`color(white)("XXXX")`is the smallest expression which is a multiple of both `(x+4)` and `(x^2+2x-8)`