Solution: The LCM of 17 and 45 is 765
Methods
How to find the LCM of 17 and 45 using Prime Factorization
One way to find the LCM of 17 and 45 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 17?
What are the Factors of 45?
Here is the prime factorization of 17:
1
7
1
17^1
1 7 1
And this is the prime factorization of 45:
3
2
×
5
1
3^2 × 5^1
3 2 × 5 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: 17, 3, 5
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 17 and 45 is 765.
How to Find the LCM of 17 and 45 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 17 and 45 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, 17 and 45:
What are the Multiples of 17?
What are the Multiples of 45?
Let’s take a look at the first 10 multiples for each of these numbers, 17 and 45:
First 10 Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170
First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450
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 17 and 45 are 765, 1530, 2295. Because 765 is the smallest, it is the least common multiple.
The LCM of 17 and 45 is 765.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 83 and 122?
What is the LCM of 77 and 64?
What is the LCM of 2 and 81?
What is the LCM of 62 and 61?
What is the LCM of 32 and 139?