Solution: The LCM of 89 and 105 is 9345
Methods
How to find the LCM of 89 and 105 using Prime Factorization
One way to find the LCM of 89 and 105 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 105?
Here is the prime factorization of 89:
8
9
1
89^1
8 9 1
And this is the prime factorization of 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 5 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: 89, 3, 5, 7
3
1
×
5
1
×
7
1
×
8
9
1
=
9345
3^1 × 5^1 × 7^1 × 89^1 = 9345
3 1 × 5 1 × 7 1 × 8 9 1 = 9345
Through this we see that the LCM of 89 and 105 is 9345.
How to Find the LCM of 89 and 105 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 89 and 105 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 105:
What are the Multiples of 89?
What are the Multiples of 105?
Let’s take a look at the first 10 multiples for each of these numbers, 89 and 105:
First 10 Multiples of 89: 89, 178, 267, 356, 445, 534, 623, 712, 801, 890
First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050
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 105 are 9345, 18690, 28035. Because 9345 is the smallest, it is the least common multiple.
The LCM of 89 and 105 is 9345.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 129 and 50?
What is the LCM of 35 and 9?
What is the LCM of 68 and 39?
What is the LCM of 108 and 11?
What is the LCM of 121 and 117?