Find the LCM 7m-21 and 14m-42

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

Since ${\displaystyle 7}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 7}$.

${\displaystyle 7}$ is a prime number

${\displaystyle 14}$ has factors of ${\displaystyle 2}$ and ${\displaystyle 7}$.

Multiply ${\displaystyle 2}$ by ${\displaystyle 7}$.

The factor for ${\displaystyle m-3}$ is ${\displaystyle m-3}$ itself.

${\displaystyle (m-3)}$ occurs ${\displaystyle 1}$ time.

The LCM of ${\displaystyle m-3,m-3}$ is the result of multiplying all factors the greatest number of times they occur in either term.