Solution: The LCM of 100 and 114 is 5700
Methods
How to find the LCM of 100 and 114 using Prime Factorization
One way to find the LCM of 100 and 114 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 100?
What are the Factors of 114?
Here is the prime factorization of 100:
2
2
×
5
2
2^2 × 5^2
2 2 × 5 2
And this 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
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, 5, 3, 19
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 100 and 114 is 5700.
How to Find the LCM of 100 and 114 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 100 and 114 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, 100 and 114:
What are the Multiples of 100?
What are the Multiples of 114?
Let’s take a look at the first 10 multiples for each of these numbers, 100 and 114:
First 10 Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
First 10 Multiples of 114: 114, 228, 342, 456, 570, 684, 798, 912, 1026, 1140
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 100 and 114 are 5700, 11400, 17100. Because 5700 is the smallest, it is the least common multiple.
The LCM of 100 and 114 is 5700.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 4 and 102?
What is the LCM of 73 and 66?
What is the LCM of 132 and 61?
What is the LCM of 114 and 140?
What is the LCM of 128 and 23?