Answer
$48$
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 $82$, $24$ and $48$.
First we write the prime factorization of each number:
$8=2\cdot 2\cdot 2$
$24=2\cdot 2\cdot 2\cdot 3$
$48=2\cdot 2\cdot 2\cdot 2\cdot 3$
Then we take each factor the greatest number of times that it appears in any one prime factorization:
$LCM=2\cdot 2\cdot 2\cdot 2\cdot 3 =48$.
The $LCM$ of the given numbers is $48$.
