# How do you find the LCM and GCF (of two or more numbers) using prime factorization (prime factor trees?)? Thanks!

Nov 3, 2017

First find all the prime factors. For GCF find all the factors that are same and multiply. For LCM find all the factors that are different, and multiply.

#### Explanation:

For GCF find the prime numbers that are shared in common and multiply. As an example 18 and 24

$18 = 2 \times 3 \times 3$
$24 = 2 \times 2 \times 2 \times 3$

There are shared factors of 2 and 3. so the GCF is

$2 \times 3 = 6$

The LCM find prime numbers that are different that are not shared and multiply.

There are 3 two's in 24 and only 1 in 18 so there are 3 two's that are not shared.
There are 2 three's in 18 and only 1 in 24 so there are 2 three's that are not shared

The LCM is
$2 \times 2 \times 2 \times 3 \times 3 = 72$