Solution: The LCM of 109 and 84 is 9156
Methods
How to find the LCM of 109 and 84 using Prime Factorization
One way to find the LCM of 109 and 84 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 84?
Here is the prime factorization of 109:
10
9
1
109^1
10 9 1
And this is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 1 × 7 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, 7
2
2
×
3
1
×
7
1
×
10
9
1
=
9156
2^2 × 3^1 × 7^1 × 109^1 = 9156
2 2 × 3 1 × 7 1 × 10 9 1 = 9156
Through this we see that the LCM of 109 and 84 is 9156.
How to Find the LCM of 109 and 84 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 109 and 84 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 84:
What are the Multiples of 109?
What are the Multiples of 84?
Let’s take a look at the first 10 multiples for each of these numbers, 109 and 84:
First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090
First 10 Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840
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 84 are 9156, 18312, 27468. Because 9156 is the smallest, it is the least common multiple.
The LCM of 109 and 84 is 9156.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 116 and 103?
What is the LCM of 113 and 61?
What is the LCM of 126 and 19?
What is the LCM of 110 and 97?
What is the LCM of 10 and 79?