# What is the least common multiple of 12, 16, 7, 2?

May 13, 2016

$336$

#### Explanation:

The prime factorisations of these numbers are:

$12 = 2 \times 2 \times 3$

$16 = 2 \times 2 \times 2 \times 2$

$7 = 7$

$2 = 2$

So the smallest number which includes all of these prime factors with these multiplicities is:

$2 \times 2 \times 2 \times 2 \times 3 \times 7 = 336$

So this is the smallest number divisible by all of $12 , 16 , 7 , 2$.