Solution: The LCM of 111 and 83 is 9213
Methods
How to find the LCM of 111 and 83 using Prime Factorization
One way to find the LCM of 111 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 111?
What are the Factors of 83?
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 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, 37, 83
3
1
×
3
7
1
×
8
3
1
=
9213
3^1 × 37^1 × 83^1 = 9213
3 1 × 3 7 1 × 8 3 1 = 9213
Through this we see that the LCM of 111 and 83 is 9213.
How to Find the LCM of 111 and 83 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 111 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, 111 and 83:
What are the Multiples of 111?
What are the Multiples of 83?
Let’s take a look at the first 10 multiples for each of these numbers, 111 and 83:
First 10 Multiples of 111: 111, 222, 333, 444, 555, 666, 777, 888, 999, 1110
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 111 and 83 are 9213, 18426, 27639. Because 9213 is the smallest, it is the least common multiple.
The LCM of 111 and 83 is 9213.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 100 and 131?
What is the LCM of 3 and 31?
What is the LCM of 114 and 110?
What is the LCM of 81 and 33?
What is the LCM of 76 and 118?