Solution: The LCM of 109 and 113 is 12317
Methods
How to find the LCM of 109 and 113 using Prime Factorization
One way to find the LCM of 109 and 113 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 109?
What are the Factors of 113?
Here is the prime factorization of 109:
10
9
1
109^1
10 9 1
And this is the prime factorization of 113:
11
3
1
113^1
11 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: 109, 113
10
9
1
×
11
3
1
=
12317
109^1 × 113^1 = 12317
10 9 1 × 11 3 1 = 12317
Through this we see that the LCM of 109 and 113 is 12317.
How to Find the LCM of 109 and 113 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 109 and 113 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, 109 and 113:
What are the Multiples of 109?
What are the Multiples of 113?
Let’s take a look at the first 10 multiples for each of these numbers, 109 and 113:
First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090
First 10 Multiples of 113: 113, 226, 339, 452, 565, 678, 791, 904, 1017, 1130
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 109 and 113 are 12317, 24634, 36951. Because 12317 is the smallest, it is the least common multiple.
The LCM of 109 and 113 is 12317.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 47 and 87?
What is the LCM of 123 and 49?
What is the LCM of 112 and 98?
What is the LCM of 65 and 4?
What is the LCM of 68 and 15?