Solution: The LCM of 38 and 109 is 4142
Methods
How to find the LCM of 38 and 109 using Prime Factorization
One way to find the LCM of 38 and 109 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 38?
What are the Factors of 109?
Here is the prime factorization of 38:
2
1
×
1
9
1
2^1 × 19^1
2 1 × 1 9 1
And this is the prime factorization of 109:
10
9
1
109^1
10 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, 19, 109
2
1
×
1
9
1
×
10
9
1
=
4142
2^1 × 19^1 × 109^1 = 4142
2 1 × 1 9 1 × 10 9 1 = 4142
Through this we see that the LCM of 38 and 109 is 4142.
How to Find the LCM of 38 and 109 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 38 and 109 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, 38 and 109:
What are the Multiples of 38?
What are the Multiples of 109?
Let’s take a look at the first 10 multiples for each of these numbers, 38 and 109:
First 10 Multiples of 38: 38, 76, 114, 152, 190, 228, 266, 304, 342, 380
First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090
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 38 and 109 are 4142, 8284, 12426. Because 4142 is the smallest, it is the least common multiple.
The LCM of 38 and 109 is 4142.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 24 and 89?
What is the LCM of 14 and 11?
What is the LCM of 74 and 113?
What is the LCM of 79 and 96?
What is the LCM of 128 and 44?