Answer
$9000$
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 $1000$ and $1125$.
First we write the prime factorization of each number:
$1000=2\cdot 2\cdot 2\cdot 5\cdot 5\cdot 5$
$1125=3\cdot 3\cdot 5\cdot 5\cdot 5$
Then we take each factor the greatest number of times that it appears in any one prime factorization:
$LCM=2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 5\cdot 5\cdot 5 = 9000$.
The $LCM$ of the given numbers is $9000$.
