Solution: The LCM of 135 and 111 is 4995
Methods
How to find the LCM of 135 and 111 using Prime Factorization
One way to find the LCM of 135 and 111 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 135?
What are the Factors of 111?
Here is the prime factorization of 135:
3
3
×
5
1
3^3 × 5^1
3 3 × 5 1
And this is the prime factorization of 111:
3
1
×
3
7
1
3^1 × 37^1
3 1 × 3 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, 37
3
3
×
5
1
×
3
7
1
=
4995
3^3 × 5^1 × 37^1 = 4995
3 3 × 5 1 × 3 7 1 = 4995
Through this we see that the LCM of 135 and 111 is 4995.
How to Find the LCM of 135 and 111 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 135 and 111 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, 135 and 111:
What are the Multiples of 135?
What are the Multiples of 111?
Let’s take a look at the first 10 multiples for each of these numbers, 135 and 111:
First 10 Multiples of 135: 135, 270, 405, 540, 675, 810, 945, 1080, 1215, 1350
First 10 Multiples of 111: 111, 222, 333, 444, 555, 666, 777, 888, 999, 1110
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 135 and 111 are 4995, 9990, 14985. Because 4995 is the smallest, it is the least common multiple.
The LCM of 135 and 111 is 4995.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 52 and 44?
What is the LCM of 43 and 78?
What is the LCM of 139 and 10?
What is the LCM of 51 and 93?
What is the LCM of 29 and 120?