Solution: The LCM of 136 and 83 is 11288
Methods
How to find the LCM of 136 and 83 using Prime Factorization
One way to find the LCM of 136 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 136?
What are the Factors of 83?
Here is the prime factorization of 136:
2
3
×
1
7
1
2^3 × 17^1
2 3 × 1 7 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: 2, 17, 83
2
3
×
1
7
1
×
8
3
1
=
11288
2^3 × 17^1 × 83^1 = 11288
2 3 × 1 7 1 × 8 3 1 = 11288
Through this we see that the LCM of 136 and 83 is 11288.
How to Find the LCM of 136 and 83 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 136 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, 136 and 83:
What are the Multiples of 136?
What are the Multiples of 83?
Let’s take a look at the first 10 multiples for each of these numbers, 136 and 83:
First 10 Multiples of 136: 136, 272, 408, 544, 680, 816, 952, 1088, 1224, 1360
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 136 and 83 are 11288, 22576, 33864. Because 11288 is the smallest, it is the least common multiple.
The LCM of 136 and 83 is 11288.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 125 and 128?
What is the LCM of 150 and 37?
What is the LCM of 126 and 85?
What is the LCM of 107 and 113?
What is the LCM of 40 and 23?