# What is the least common multiple of {120, 124, 165}?

$40 , 920$

#### Explanation:

To find the least common multiple, let's do a prime factorization on these numbers:

$120 = 2 \times 2 \times 2 \times 3 \times 5$
$124 = 2 \times 2 \times 31$
$165 = 3 \times 5 \times 11$

To find the lowest common multiple, we take the largest group of primes we can choose from.

For instance, the first prime is 2. The 120 has 3 of them and that is the most that any of our other numbers have. So we need 3 2s.

$2 \times 2 \times 2 \times \ldots$

For 3, the next prime, two of the numbers have a 3, so we need 1 also.

$2 \times 2 \times 2 \times 3 \times \ldots$

We also have two numbers with a 5 each:

$2 \times 2 \times 2 \times 3 \times 5 \times \ldots$

And there is an 11 and a 31:

$2 \times 2 \times 2 \times 3 \times 5 \times 11 \times 31 = 40 , 920$

$120 \times 11 \times 31 = 40 , 920$
$124 \times 2 \times 3 \times 5 \times 11 = 40 , 920$
$165 \times 2 \times 2 \times 2 \times 31 = 40 , 920$