Solution: The LCM of 45 and 7 is 315
Methods
How to find the LCM of 45 and 7 using Prime Factorization
One way to find the LCM of 45 and 7 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 7?
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 7:
7
1
7^1
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, 7
3
2
×
5
1
×
7
1
=
315
3^2 × 5^1 × 7^1 = 315
3 2 × 5 1 × 7 1 = 315
Through this we see that the LCM of 45 and 7 is 315.
How to Find the LCM of 45 and 7 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 45 and 7 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 7:
What are the Multiples of 45?
What are the Multiples of 7?
Let’s take a look at the first 10 multiples for each of these numbers, 45 and 7:
First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450
First 10 Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
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 7 are 315, 630, 945. Because 315 is the smallest, it is the least common multiple.
The LCM of 45 and 7 is 315.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 15 and 144?
What is the LCM of 101 and 126?
What is the LCM of 61 and 47?
What is the LCM of 142 and 62?
What is the LCM of 75 and 10?