# How do you find the LCM of x^2+9x+18, x+3?

May 29, 2017

LCM is $\left(x + 3\right) \left(x + 6\right) = {x}^{2} + 9 x + 18$

#### Explanation:

For finding LCM (or HCF) of two or more polynomials, just factorize the polynomials and then considering each factor a different number , proceed to find LCM (or GCF) as one proceeds with numbers.

Here ${x}^{2} + 9 x + 18 = {x}^{2} + 6 x + 3 x + 18 = x \left(x + 6\right) + 3 \left(x + 6\right) = \left(x + 3\right) \left(x + 6\right)$ and there are no further factors of second polynomial $\left(x + 3\right)$

As such we have $\left(x + 3\right) \left(x + 6\right)$ and $\left(x + 3\right)$

We have $\left(x + 3\right)$ as common factor and after taking out $\left(x + 3\right)$,

we are left with $\left(x + 6\right)$

Hence, LCM is $\left(x + 3\right) \left(x + 6\right) = {x}^{2} + 9 x + 18$