Find the LCM 2n-10 , 4n-20

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 ${\displaystyle 2}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 2}$.

${\displaystyle 2}$ is a prime number

${\displaystyle 4}$ has factors of ${\displaystyle 2}$ and ${\displaystyle 2}$.

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

The factor for ${\displaystyle n-5}$ is ${\displaystyle n-5}$ itself.

${\displaystyle (n-5)}$ occurs ${\displaystyle 1}$ time.

The LCM of ${\displaystyle n-5,n-5}$ is the result of multiplying all factors the greatest number of times they occur in either term.