# How do you find the LCM of (x-1)(x+2) and (x-1)(x+3)?

##### 1 Answer
Nov 29, 2017

The LCM is $\left(x - 1\right) \left(x + 2\right) \left(x + 3\right)$

#### Explanation:

Remember that you can find the LCM between two expressions by multiplying them, and then dividing it with their GCF.

$\left(x - 1\right) \left(x + 2\right) \left(x - 1\right) \left(x + 3\right)$ is the product

Now, it is important to see that $\left(x - 1\right) \left(x + 2\right)$ and $\left(x - 1\right) \left(x + 3\right)$ share $\left(x - 1\right)$ as their greatest common factor.

Therefore, we divide $\left(x - 1\right) \left(x + 2\right) \left(x - 1\right) \left(x + 3\right)$ by $\left(x - 1\right)$. $\frac{\left(x - 1\right) \left(x + 2\right) \left(x - 1\right) \left(x + 3\right)}{\left(x - 1\right)} = \left(x - 1\right) \left(x + 2\right) \left(x + 3\right)$