Solution: The LCM of 111 and 45 is 1665
Methods
How to find the LCM of 111 and 45 using Prime Factorization
One way to find the LCM of 111 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 111?
What are the Factors of 45?
Here is the prime factorization of 111:
3
1
×
3
7
1
3^1 × 37^1
3 1 × 3 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: 3, 37, 5
3
2
×
5
1
×
3
7
1
=
1665
3^2 × 5^1 × 37^1 = 1665
3 2 × 5 1 × 3 7 1 = 1665
Through this we see that the LCM of 111 and 45 is 1665.
How to Find the LCM of 111 and 45 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 111 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, 111 and 45:
What are the Multiples of 111?
What are the Multiples of 45?
Let’s take a look at the first 10 multiples for each of these numbers, 111 and 45:
First 10 Multiples of 111: 111, 222, 333, 444, 555, 666, 777, 888, 999, 1110
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 111 and 45 are 1665, 3330, 4995. Because 1665 is the smallest, it is the least common multiple.
The LCM of 111 and 45 is 1665.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 115 and 60?
What is the LCM of 34 and 55?
What is the LCM of 101 and 130?
What is the LCM of 40 and 112?
What is the LCM of 106 and 83?