# Question #99e5b

Feb 8, 2017

$G C F = 4 \mathmr{and} L C M = 180 x y$

#### Explanation:

Write each as the product of its prime factors:

$\textcolor{w h i t e}{\ldots . .} 20 y = \textcolor{b l u e}{2 \times 2} \textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \times 5 \times y$
$\textcolor{w h i t e}{\ldots . .} 36 x = \textcolor{b l u e}{2 \times 2} \times 3 \times 3 \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \times x$

$\text{ } G C F = \textcolor{b l u e}{2 \times 2} = 4$

$\text{ } L C M = 2 \times 2 \times 3 \times 3 \times 5 \times y \times x = 180 x y$

NOte that for the LCM we need all the factors, but without duplicates.

For the GCF, we include all the factors they have in common and multiply them together.