Solution: The LCM of 28 and 129 is 3612
Methods
How to find the LCM of 28 and 129 using Prime Factorization
One way to find the LCM of 28 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 28?
What are the Factors of 129?
Here is the prime factorization of 28:
2
2
×
7
1
2^2 × 7^1
2 2 × 7 1
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, 7, 3, 43
2
2
×
3
1
×
7
1
×
4
3
1
=
3612
2^2 × 3^1 × 7^1 × 43^1 = 3612
2 2 × 3 1 × 7 1 × 4 3 1 = 3612
Through this we see that the LCM of 28 and 129 is 3612.
How to Find the LCM of 28 and 129 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 28 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, 28 and 129:
What are the Multiples of 28?
What are the Multiples of 129?
Let’s take a look at the first 10 multiples for each of these numbers, 28 and 129:
First 10 Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280
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 28 and 129 are 3612, 7224, 10836. Because 3612 is the smallest, it is the least common multiple.
The LCM of 28 and 129 is 3612.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 145 and 53?
What is the LCM of 120 and 7?
What is the LCM of 90 and 137?
What is the LCM of 49 and 12?
What is the LCM of 110 and 17?