Solution: The LCM of 81 and 107 is 8667
Methods
How to find the LCM of 81 and 107 using Prime Factorization
One way to find the LCM of 81 and 107 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 81?
What are the Factors of 107?
Here is the prime factorization of 81:
3
4
3^4
3 4
And this is the prime factorization of 107:
10
7
1
107^1
10 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: 3, 107
3
4
×
10
7
1
=
8667
3^4 × 107^1 = 8667
3 4 × 10 7 1 = 8667
Through this we see that the LCM of 81 and 107 is 8667.
How to Find the LCM of 81 and 107 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 81 and 107 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, 81 and 107:
What are the Multiples of 81?
What are the Multiples of 107?
Let’s take a look at the first 10 multiples for each of these numbers, 81 and 107:
First 10 Multiples of 81: 81, 162, 243, 324, 405, 486, 567, 648, 729, 810
First 10 Multiples of 107: 107, 214, 321, 428, 535, 642, 749, 856, 963, 1070
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 81 and 107 are 8667, 17334, 26001. Because 8667 is the smallest, it is the least common multiple.
The LCM of 81 and 107 is 8667.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 124 and 60?
What is the LCM of 22 and 31?
What is the LCM of 99 and 78?
What is the LCM of 114 and 42?
What is the LCM of 29 and 50?