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.