Solution: The LCM of 116 and 35 is 4060
Methods
How to find the LCM of 116 and 35 using Prime Factorization
One way to find the LCM of 116 and 35 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 116?
What are the Factors of 35?
Here is the prime factorization of 116:
2
2
×
2
9
1
2^2 × 29^1
2 2 × 2 9 1
And this is the prime factorization of 35:
5
1
×
7
1
5^1 × 7^1
5 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: 2, 29, 5, 7
2
2
×
5
1
×
7
1
×
2
9
1
=
4060
2^2 × 5^1 × 7^1 × 29^1 = 4060
2 2 × 5 1 × 7 1 × 2 9 1 = 4060
Through this we see that the LCM of 116 and 35 is 4060.
How to Find the LCM of 116 and 35 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 116 and 35 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, 116 and 35:
What are the Multiples of 116?
What are the Multiples of 35?
Let’s take a look at the first 10 multiples for each of these numbers, 116 and 35:
First 10 Multiples of 116: 116, 232, 348, 464, 580, 696, 812, 928, 1044, 1160
First 10 Multiples of 35: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350
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 116 and 35 are 4060, 8120, 12180. Because 4060 is the smallest, it is the least common multiple.
The LCM of 116 and 35 is 4060.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 146 and 113?
What is the LCM of 26 and 56?
What is the LCM of 50 and 145?
What is the LCM of 13 and 86?
What is the LCM of 29 and 76?