Solution: The LCM of 113 and 68 is 7684
Methods
How to find the LCM of 113 and 68 using Prime Factorization
One way to find the LCM of 113 and 68 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 113?
What are the Factors of 68?
Here is the prime factorization of 113:
11
3
1
113^1
11 3 1
And this is the prime factorization of 68:
2
2
×
1
7
1
2^2 × 17^1
2 2 × 1 7 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: 113, 2, 17
2
2
×
1
7
1
×
11
3
1
=
7684
2^2 × 17^1 × 113^1 = 7684
2 2 × 1 7 1 × 11 3 1 = 7684
Through this we see that the LCM of 113 and 68 is 7684.
How to Find the LCM of 113 and 68 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 113 and 68 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, 113 and 68:
What are the Multiples of 113?
What are the Multiples of 68?
Let’s take a look at the first 10 multiples for each of these numbers, 113 and 68:
First 10 Multiples of 113: 113, 226, 339, 452, 565, 678, 791, 904, 1017, 1130
First 10 Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680
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 113 and 68 are 7684, 15368, 23052. Because 7684 is the smallest, it is the least common multiple.
The LCM of 113 and 68 is 7684.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 106 and 134?
What is the LCM of 79 and 27?
What is the LCM of 34 and 28?
What is the LCM of 17 and 96?
What is the LCM of 107 and 80?