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

Jun 14, 2015

${x}^{2} + 2 x - 8$ is the Least Common Multiple

#### Explanation:

Since $x + 4$ is a factor of ${x}^{2} + 2 x - 8$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$(${x}^{2} + 2 x - 8 = \left(x + 4\right) \left(x - 2\right)$)
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 $\left({x}^{2} + 2 x - 8\right)$)

${x}^{2} + 2 x - 8$
$\textcolor{w h i t e}{\text{XXXX}}$is the smallest expression which is a multiple of both $\left(x + 4\right)$ and $\left({x}^{2} + 2 x - 8\right)$