Solution: The LCM of 54 and 129 is 2322
Methods
How to find the LCM of 54 and 129 using Prime Factorization
One way to find the LCM of 54 and 129 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 129?
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 129:
3
1
×
4
3
1
3^1 × 43^1
3 1 × 4 3 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, 43
2
1
×
3
3
×
4
3
1
=
2322
2^1 × 3^3 × 43^1 = 2322
2 1 × 3 3 × 4 3 1 = 2322
Through this we see that the LCM of 54 and 129 is 2322.
How to Find the LCM of 54 and 129 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 54 and 129 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 129:
What are the Multiples of 54?
What are the Multiples of 129?
Let’s take a look at the first 10 multiples for each of these numbers, 54 and 129:
First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540
First 10 Multiples of 129: 129, 258, 387, 516, 645, 774, 903, 1032, 1161, 1290
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 129 are 2322, 4644, 6966. Because 2322 is the smallest, it is the least common multiple.
The LCM of 54 and 129 is 2322.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 43 and 129?
What is the LCM of 89 and 57?
What is the LCM of 92 and 50?
What is the LCM of 147 and 141?
What is the LCM of 27 and 126?