Solution: The LCM of 45 and 83 is 3735
Methods
How to find the LCM of 45 and 83 using Prime Factorization
One way to find the LCM of 45 and 83 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 83?
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 83:
8
3
1
83^1
8 3 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, 83
3
2
×
5
1
×
8
3
1
=
3735
3^2 × 5^1 × 83^1 = 3735
3 2 × 5 1 × 8 3 1 = 3735
Through this we see that the LCM of 45 and 83 is 3735.
How to Find the LCM of 45 and 83 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 45 and 83 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 83:
What are the Multiples of 45?
What are the Multiples of 83?
Let’s take a look at the first 10 multiples for each of these numbers, 45 and 83:
First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450
First 10 Multiples of 83: 83, 166, 249, 332, 415, 498, 581, 664, 747, 830
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 83 are 3735, 7470, 11205. Because 3735 is the smallest, it is the least common multiple.
The LCM of 45 and 83 is 3735.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 52 and 46?
What is the LCM of 59 and 43?
What is the LCM of 148 and 44?
What is the LCM of 75 and 21?
What is the LCM of 109 and 140?