Solution: The LCM of 135 and 83 is 11205
Methods
How to find the LCM of 135 and 83 using Prime Factorization
One way to find the LCM of 135 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 135?
What are the Factors of 83?
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 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
3
×
5
1
×
8
3
1
=
11205
3^3 × 5^1 × 83^1 = 11205
3 3 × 5 1 × 8 3 1 = 11205
Through this we see that the LCM of 135 and 83 is 11205.
How to Find the LCM of 135 and 83 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 135 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, 135 and 83:
What are the Multiples of 135?
What are the Multiples of 83?
Let’s take a look at the first 10 multiples for each of these numbers, 135 and 83:
First 10 Multiples of 135: 135, 270, 405, 540, 675, 810, 945, 1080, 1215, 1350
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 135 and 83 are 11205, 22410, 33615. Because 11205 is the smallest, it is the least common multiple.
The LCM of 135 and 83 is 11205.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 68 and 134?
What is the LCM of 142 and 139?
What is the LCM of 62 and 84?
What is the LCM of 40 and 95?
What is the LCM of 138 and 34?