Solution: The LCM of 89 and 93 is 8277
Methods
How to find the LCM of 89 and 93 using Prime Factorization
One way to find the LCM of 89 and 93 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 89?
What are the Factors of 93?
Here is the prime factorization of 89:
8
9
1
89^1
8 9 1
And this is the prime factorization of 93:
3
1
×
3
1
1
3^1 × 31^1
3 1 × 3 1 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: 89, 3, 31
3
1
×
3
1
1
×
8
9
1
=
8277
3^1 × 31^1 × 89^1 = 8277
3 1 × 3 1 1 × 8 9 1 = 8277
Through this we see that the LCM of 89 and 93 is 8277.
How to Find the LCM of 89 and 93 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 89 and 93 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, 89 and 93:
What are the Multiples of 89?
What are the Multiples of 93?
Let’s take a look at the first 10 multiples for each of these numbers, 89 and 93:
First 10 Multiples of 89: 89, 178, 267, 356, 445, 534, 623, 712, 801, 890
First 10 Multiples of 93: 93, 186, 279, 372, 465, 558, 651, 744, 837, 930
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 89 and 93 are 8277, 16554, 24831. Because 8277 is the smallest, it is the least common multiple.
The LCM of 89 and 93 is 8277.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 125 and 144?
What is the LCM of 132 and 3?
What is the LCM of 87 and 44?
What is the LCM of 38 and 141?
What is the LCM of 41 and 109?