Solution: The LCM of 45 and 61 is 2745
Methods
How to find the LCM of 45 and 61 using Prime Factorization
One way to find the LCM of 45 and 61 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 61?
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 61:
6
1
1
61^1
6 1 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, 61
3
2
×
5
1
×
6
1
1
=
2745
3^2 × 5^1 × 61^1 = 2745
3 2 × 5 1 × 6 1 1 = 2745
Through this we see that the LCM of 45 and 61 is 2745.
How to Find the LCM of 45 and 61 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 45 and 61 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 61:
What are the Multiples of 45?
What are the Multiples of 61?
Let’s take a look at the first 10 multiples for each of these numbers, 45 and 61:
First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450
First 10 Multiples of 61: 61, 122, 183, 244, 305, 366, 427, 488, 549, 610
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 61 are 2745, 5490, 8235. Because 2745 is the smallest, it is the least common multiple.
The LCM of 45 and 61 is 2745.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 146 and 140?
What is the LCM of 97 and 148?
What is the LCM of 14 and 92?
What is the LCM of 78 and 77?
What is the LCM of 29 and 91?