# What is the least common multiple of {9, 36, 25, 45}?

May 9, 2016

$900$

#### Explanation:

Given: $\left\{9 , 36 , 25 , 45\right\}$

First find the prime factorisations of all of the numbers:

$\left\{\begin{matrix}9 = 3 \times 3 \\ 36 = 2 \times 2 \times 3 \times 3 \\ 25 = 5 \times 5 \\ 45 = 3 \times 3 \times 5\end{matrix}\right.$

The smallest number that contains all of these prime factors in the multiplicities in which they occur in each of these numbers is:

$2 \times 2 \times 3 \times 3 \times 5 \times 5 = 900$

So this is the least common multiple.