Solution: The LCM of 20 and 109 is 2180
Methods
How to find the LCM of 20 and 109 using Prime Factorization
One way to find the LCM of 20 and 109 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 20?
What are the Factors of 109?
Here is the prime factorization of 20:
2
2
×
5
1
2^2 × 5^1
2 2 × 5 1
And this is the prime factorization of 109:
10
9
1
109^1
10 9 1
When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 2, 5, 109
2
2
×
5
1
×
10
9
1
=
2180
2^2 × 5^1 × 109^1 = 2180
2 2 × 5 1 × 10 9 1 = 2180
Through this we see that the LCM of 20 and 109 is 2180.
How to Find the LCM of 20 and 109 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 20 and 109 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.
Let’s take a look at the multiples for each of these numbers, 20 and 109:
What are the Multiples of 20?
What are the Multiples of 109?
Let’s take a look at the first 10 multiples for each of these numbers, 20 and 109:
First 10 Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200
First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090
You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 20 and 109 are 2180, 4360, 6540. Because 2180 is the smallest, it is the least common multiple.
The LCM of 20 and 109 is 2180.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 101 and 114?
What is the LCM of 96 and 18?
What is the LCM of 126 and 86?
What is the LCM of 113 and 142?
What is the LCM of 108 and 79?