Solution: The LCM of 116 and 74 is 4292
Methods
How to find the LCM of 116 and 74 using Prime Factorization
One way to find the LCM of 116 and 74 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 74?
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 74:
2
1
×
3
7
1
2^1 × 37^1
2 1 × 3 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, 37
2
2
×
2
9
1
×
3
7
1
=
4292
2^2 × 29^1 × 37^1 = 4292
2 2 × 2 9 1 × 3 7 1 = 4292
Through this we see that the LCM of 116 and 74 is 4292.
How to Find the LCM of 116 and 74 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 116 and 74 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 74:
What are the Multiples of 116?
What are the Multiples of 74?
Let’s take a look at the first 10 multiples for each of these numbers, 116 and 74:
First 10 Multiples of 116: 116, 232, 348, 464, 580, 696, 812, 928, 1044, 1160
First 10 Multiples of 74: 74, 148, 222, 296, 370, 444, 518, 592, 666, 740
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 74 are 4292, 8584, 12876. Because 4292 is the smallest, it is the least common multiple.
The LCM of 116 and 74 is 4292.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 37 and 2?
What is the LCM of 132 and 23?
What is the LCM of 48 and 8?
What is the LCM of 13 and 49?
What is the LCM of 20 and 112?