# Using Prime Factorization to Find LCM

From my previous lesson, I went over the steps on how to find the LCM of two positive integers using the List Method. This time I will focus on the method where Prime Factorization is used to find the LCM.

I highly recommend that you review the procedure on how to perform Prime Factorization because this skill will play a major role in this lesson. Check out the following link: Integer Prime Factorization.

## Steps on How to Find the LCM using Prime Factorization

**Step 1:** Perform the prime factorization of each number then write it in exponential form. Align the common prime factor base whenever possible.

**Step 2:** For the numbers with a common prime factor base, select the prime number that has the highest power. The prime factor with the highest power implies that it occurs the most in the entire list.

**Step 3:** If a distinct prime factor has **NO** matching prime factor base in the list, immediately include this factor with its exponent in the collection of numbers that you will multiply later.

** Note:** Steps #2 and #3 ensure that all distinct prime factors in the ENTIRE list are represented without duplicates.

**Step 4: **To determine the Least Common Multiple (LCM), multiply all the numbers that you have collected or gathered from steps #2 and #3.

## Examples of Determining the Least Common Multiple (LCM) using Prime Factorization

**Example 1: **What is the LCM of **12 **and **90** ?

First, write the prime factorization of each number in exponential form.