Solution: The LCM of 36 and 20 is 180
Methods
How to find the LCM of 36 and 20 using Prime Factorization
One way to find the LCM of 36 and 20 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 36?
What are the Factors of 20?
Here is the prime factorization of 36:
2
2
×
3
2
2^2 × 3^2
2 2 × 3 2
And this is the prime factorization of 20:
2
2
×
5
1
2^2 × 5^1
2 2 × 5 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, 3, 5
2
2
×
3
2
×
5
1
=
180
2^2 × 3^2 × 5^1 = 180
2 2 × 3 2 × 5 1 = 180
Through this we see that the LCM of 36 and 20 is 180.
How to Find the LCM of 36 and 20 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 36 and 20 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, 36 and 20:
What are the Multiples of 36?
What are the Multiples of 20?
Let’s take a look at the first 10 multiples for each of these numbers, 36 and 20:
First 10 Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360
First 10 Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200
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 36 and 20 are 180, 360, 540. Because 180 is the smallest, it is the least common multiple.
The LCM of 36 and 20 is 180.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 147 and 34?
What is the LCM of 39 and 111?
What is the LCM of 5 and 96?
What is the LCM of 52 and 94?
What is the LCM of 12 and 72?