Solution: The LCM of 100 and 123 is 12300
Methods
How to find the LCM of 100 and 123 using Prime Factorization
One way to find the LCM of 100 and 123 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 123?
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 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 1 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, 41
2
2
×
3
1
×
5
2
×
4
1
1
=
12300
2^2 × 3^1 × 5^2 × 41^1 = 12300
2 2 × 3 1 × 5 2 × 4 1 1 = 12300
Through this we see that the LCM of 100 and 123 is 12300.
How to Find the LCM of 100 and 123 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 100 and 123 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 123:
What are the Multiples of 100?
What are the Multiples of 123?
Let’s take a look at the first 10 multiples for each of these numbers, 100 and 123:
First 10 Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
First 10 Multiples of 123: 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230
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 123 are 12300, 24600, 36900. Because 12300 is the smallest, it is the least common multiple.
The LCM of 100 and 123 is 12300.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 38 and 1?
What is the LCM of 134 and 123?
What is the LCM of 52 and 5?
What is the LCM of 29 and 120?
What is the LCM of 34 and 94?