Solution: The LCM of 108 and 19 is 2052
Methods
How to find the LCM of 108 and 19 using Prime Factorization
One way to find the LCM of 108 and 19 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 108?
What are the Factors of 19?
Here is the prime factorization of 108:
2
2
×
3
3
2^2 × 3^3
2 2 × 3 3
And this is the prime factorization of 19:
1
9
1
19^1
1 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, 19
2
2
×
3
3
×
1
9
1
=
2052
2^2 × 3^3 × 19^1 = 2052
2 2 × 3 3 × 1 9 1 = 2052
Through this we see that the LCM of 108 and 19 is 2052.
How to Find the LCM of 108 and 19 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 108 and 19 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, 108 and 19:
What are the Multiples of 108?
What are the Multiples of 19?
Let’s take a look at the first 10 multiples for each of these numbers, 108 and 19:
First 10 Multiples of 108: 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080
First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190
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 108 and 19 are 2052, 4104, 6156. Because 2052 is the smallest, it is the least common multiple.
The LCM of 108 and 19 is 2052.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 127 and 138?
What is the LCM of 67 and 6?
What is the LCM of 141 and 58?
What is the LCM of 12 and 19?
What is the LCM of 21 and 134?