Solution: The LCM of 59 and 113 is 6667
Methods
How to find the LCM of 59 and 113 using Prime Factorization
One way to find the LCM of 59 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 59?
What are the Factors of 113?
Here is the prime factorization of 59:
5
9
1
59^1
5 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: 59, 113
5
9
1
×
11
3
1
=
6667
59^1 × 113^1 = 6667
5 9 1 × 11 3 1 = 6667
Through this we see that the LCM of 59 and 113 is 6667.
How to Find the LCM of 59 and 113 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 59 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, 59 and 113:
What are the Multiples of 59?
What are the Multiples of 113?
Let’s take a look at the first 10 multiples for each of these numbers, 59 and 113:
First 10 Multiples of 59: 59, 118, 177, 236, 295, 354, 413, 472, 531, 590
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 59 and 113 are 6667, 13334, 20001. Because 6667 is the smallest, it is the least common multiple.
The LCM of 59 and 113 is 6667.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 48 and 104?
What is the LCM of 92 and 26?
What is the LCM of 38 and 37?
What is the LCM of 124 and 61?
What is the LCM of 133 and 131?