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

1 Answer

#40,920#

Explanation:

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#