Solution: The LCM of 114 and 100 is 5700
Methods
How to find the LCM of 114 and 100 using Prime Factorization
One way to find the LCM of 114 and 100 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 114?
What are the Factors of 100?
Here is the prime factorization of 114:
2
1
×
3
1
×
1
9
1
2^1 × 3^1 × 19^1
2 1 × 3 1 × 1 9 1
And this is the prime factorization of 100:
2
2
×
5
2
2^2 × 5^2
2 2 × 5 2
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, 3, 19, 5
2
2
×
3
1
×
5
2
×
1
9
1
=
5700
2^2 × 3^1 × 5^2 × 19^1 = 5700
2 2 × 3 1 × 5 2 × 1 9 1 = 5700
Through this we see that the LCM of 114 and 100 is 5700.
How to Find the LCM of 114 and 100 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 114 and 100 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, 114 and 100:
What are the Multiples of 114?
What are the Multiples of 100?
Let’s take a look at the first 10 multiples for each of these numbers, 114 and 100:
First 10 Multiples of 114: 114, 228, 342, 456, 570, 684, 798, 912, 1026, 1140
First 10 Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
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 114 and 100 are 5700, 11400, 17100. Because 5700 is the smallest, it is the least common multiple.
The LCM of 114 and 100 is 5700.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 31 and 58?
What is the LCM of 137 and 84?
What is the LCM of 139 and 128?
What is the LCM of 101 and 38?
What is the LCM of 4 and 65?