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

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Answer 1 · 2018-03-06T05:21:25

$40,920$

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

$120=2xx2xx2xx3xx5$
$124=2xx2xx31$
$165=3xx5xx11$

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.

$2xx2xx2xx...$

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

$2xx2xx2xx3xx...$

We also have two numbers with a 5 each:

$2xx2xx2xx3xx5xx...$

And there is an 11 and a 31:

$2xx2xx2xx3xx5xx11xx31=40,920$

$120xx11xx31=40,920$
$124xx2xx3xx5xx11=40,920$
$165xx2xx2xx2xx31=40,920$

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