Solution: The LCM of 138 and 79 is 10902
Methods
How to find the LCM of 138 and 79 using Prime Factorization
One way to find the LCM of 138 and 79 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 138?
What are the Factors of 79?
Here is the prime factorization of 138:
2
1
×
3
1
×
2
3
1
2^1 × 3^1 × 23^1
2 1 × 3 1 × 2 3 1
And this is the prime factorization of 79:
7
9
1
79^1
7 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, 23, 79
2
1
×
3
1
×
2
3
1
×
7
9
1
=
10902
2^1 × 3^1 × 23^1 × 79^1 = 10902
2 1 × 3 1 × 2 3 1 × 7 9 1 = 10902
Through this we see that the LCM of 138 and 79 is 10902.
How to Find the LCM of 138 and 79 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 138 and 79 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, 138 and 79:
What are the Multiples of 138?
What are the Multiples of 79?
Let’s take a look at the first 10 multiples for each of these numbers, 138 and 79:
First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380
First 10 Multiples of 79: 79, 158, 237, 316, 395, 474, 553, 632, 711, 790
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 138 and 79 are 10902, 21804, 32706. Because 10902 is the smallest, it is the least common multiple.
The LCM of 138 and 79 is 10902.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 48 and 100?
What is the LCM of 99 and 20?
What is the LCM of 43 and 130?
What is the LCM of 30 and 78?
What is the LCM of 40 and 6?