Answer
$360$
Work Step by Step
The least common multiple ($LCM$) of two numbers $a$ and $b$ is the smallest number which is a multiple of both numbers $a$ and $b$.
We have to determine the $LCM$ of the numbers $40$ and $90$.
First we write the prime factorization of each number:
$40=2\cdot 2\cdot 2\cdot 5$
$90=2\cdot 3\cdot 3\cdot 5$
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 $360$.
