Answer
$360$
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 $8$, $18$ and $30$.
First we write the prime factorization of each number:
$8=2\cdot 2\cdot 2$
$18=2\cdot 3\cdot 3$
$30=2\cdot 3\cdot 5$
Then we take each factor the greatest number of times that it appears in any one prime factorization:
$LCM=2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 5 =360$.
The $LCM$ of the given numbers is $360$.
