# What is the LCM of 24a, 32a^4?

Oct 17, 2015

$L C M \left(24 a , 32 {a}^{4}\right) = \frac{24 a \cdot 32 {a}^{4}}{G C D \left(24 a , 32 {a}^{4}\right)} = 96 {a}^{4}$

#### Explanation:

The GCD (Greatest Common Divisor) of $24$ and $32$ is $8$

The GCD of $a$ and ${a}^{4}$ is $a$

Therefore
$\textcolor{w h i t e}{\text{XXX}} G C D \left(24 a , 32 {a}^{4}\right) = 8 a$
and
$\textcolor{w h i t e}{\text{XXX}} L C M \left(24 a , 32 {a}^{4}\right) = \frac{24 a \cdot 32 {a}^{4}}{8 a}$

$\textcolor{w h i t e}{\text{XXXXXXXXXXXXX}} = 96 {a}^{4}$