Solution: The LCM of 54 and 90 is 270
Methods
How to find the LCM of 54 and 90 using Prime Factorization
One way to find the LCM of 54 and 90 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 54?
What are the Factors of 90?
Here is the prime factorization of 54:
2
1
×
3
3
2^1 × 3^3
2 1 × 3 3
And this is the prime factorization of 90:
2
1
×
3
2
×
5
1
2^1 × 3^2 × 5^1
2 1 × 3 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
1
×
3
3
×
5
1
=
270
2^1 × 3^3 × 5^1 = 270
2 1 × 3 3 × 5 1 = 270
Through this we see that the LCM of 54 and 90 is 270.
How to Find the LCM of 54 and 90 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 54 and 90 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, 54 and 90:
What are the Multiples of 54?
What are the Multiples of 90?
Let’s take a look at the first 10 multiples for each of these numbers, 54 and 90:
First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540
First 10 Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900
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 54 and 90 are 270, 540, 810. Because 270 is the smallest, it is the least common multiple.
The LCM of 54 and 90 is 270.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 86 and 83?
What is the LCM of 141 and 93?
What is the LCM of 70 and 23?
What is the LCM of 97 and 144?
What is the LCM of 82 and 30?