# What is the least common multiple of #{8, 12, 16, 3}?

48

#### Explanation:

Let's first do prime factorizations:

$8 = {2}^{3}$

$12 = {2}^{2} \times 3$

$16 = {2}^{4}$

$3 = 3$

Now we look for the largest grouping of each prime in the factorizations.

For the number 2, the largest grouping is in 16:

$L C M = {2}^{4} \times \ldots$

The other prime factor is 3. We need one of those (since both 12 and 3 only have one):

$L C M = {2}^{4} \times 3 = 48$