Solution: The LCM of 109 and 138 is 15042
Methods
How to find the LCM of 109 and 138 using Prime Factorization
One way to find the LCM of 109 and 138 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 109?
What are the Factors of 138?
Here is the prime factorization of 109:
10
9
1
109^1
10 9 1
And this 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
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: 109, 2, 3, 23
2
1
×
3
1
×
2
3
1
×
10
9
1
=
15042
2^1 × 3^1 × 23^1 × 109^1 = 15042
2 1 × 3 1 × 2 3 1 × 10 9 1 = 15042
Through this we see that the LCM of 109 and 138 is 15042.
How to Find the LCM of 109 and 138 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 109 and 138 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, 109 and 138:
What are the Multiples of 109?
What are the Multiples of 138?
Let’s take a look at the first 10 multiples for each of these numbers, 109 and 138:
First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090
First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380
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 109 and 138 are 15042, 30084, 45126. Because 15042 is the smallest, it is the least common multiple.
The LCM of 109 and 138 is 15042.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 132 and 23?
What is the LCM of 90 and 89?
What is the LCM of 18 and 28?
What is the LCM of 107 and 38?
What is the LCM of 60 and 66?