Question

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

Answer 1

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 xx 3 xx 3`
`24 = 2 xx 2 xx 2 xx 3`

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

`2 xx 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 xx 2 xx 2 xx 3 xx 3 = 72`