Find the LCM 10 , 3 , 6

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.

${\displaystyle 10}$ has factors of ${\displaystyle 2}$ and ${\displaystyle 5}$.

Since ${\displaystyle 3}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 3}$.

${\displaystyle 3}$ is a prime number

${\displaystyle 6}$ has factors of ${\displaystyle 2}$ and ${\displaystyle 3}$.

The LCM of ${\displaystyle 10,3,6}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.