Solution: The LCM of 45 and 85 is 765
Methods
How to find the LCM of 45 and 85 using Prime Factorization
One way to find the LCM of 45 and 85 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 45?
What are the Factors of 85?
Here is the prime factorization of 45:
3
2
×
5
1
3^2 × 5^1
3 2 × 5 1
And this is the prime factorization of 85:
5
1
×
1
7
1
5^1 × 17^1
5 1 × 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: 3, 5, 17
3
2
×
5
1
×
1
7
1
=
765
3^2 × 5^1 × 17^1 = 765
3 2 × 5 1 × 1 7 1 = 765
Through this we see that the LCM of 45 and 85 is 765.
How to Find the LCM of 45 and 85 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 45 and 85 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, 45 and 85:
What are the Multiples of 45?
What are the Multiples of 85?
Let’s take a look at the first 10 multiples for each of these numbers, 45 and 85:
First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450
First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850
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 45 and 85 are 765, 1530, 2295. Because 765 is the smallest, it is the least common multiple.
The LCM of 45 and 85 is 765.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 60 and 8?
What is the LCM of 102 and 131?
What is the LCM of 110 and 37?
What is the LCM of 38 and 51?
What is the LCM of 103 and 97?