Solution: The LCM of 54 and 114 is 1026
Methods
How to find the LCM of 54 and 114 using Prime Factorization
One way to find the LCM of 54 and 114 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 114?
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 114:
2
1
×
3
1
×
1
9
1
2^1 × 3^1 × 19^1
2 1 × 3 1 × 1 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, 3, 19
2
1
×
3
3
×
1
9
1
=
1026
2^1 × 3^3 × 19^1 = 1026
2 1 × 3 3 × 1 9 1 = 1026
Through this we see that the LCM of 54 and 114 is 1026.
How to Find the LCM of 54 and 114 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 54 and 114 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 114:
What are the Multiples of 54?
What are the Multiples of 114?
Let’s take a look at the first 10 multiples for each of these numbers, 54 and 114:
First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540
First 10 Multiples of 114: 114, 228, 342, 456, 570, 684, 798, 912, 1026, 1140
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 114 are 1026, 2052, 3078. Because 1026 is the smallest, it is the least common multiple.
The LCM of 54 and 114 is 1026.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 28 and 87?
What is the LCM of 78 and 116?
What is the LCM of 139 and 147?
What is the LCM of 150 and 51?
What is the LCM of 81 and 140?