Answer
$ 72$
Work Step by Step
The least common multiple ($LCM$) of a set of numbers is the smallest number which is a multiple of each number in the set.
We have to determine the $LCM$ of the numbers $9$, $36$ and $72$.
First we write the prime factorization of each number:
$9=3\cdot 3$
$36=2\cdot 2\cdot 3\cdot 3$
$72=2\cdot 2\cdot 2\cdot 3\cdot 3$
Then we take each factor the greatest number of times that it appears in any one prime factorization:
$LCM=2\cdot 2\cdot 2\cdot 3\cdot 3 =72$.
The $LCM$ of the given numbers is $72$.
