Solution: The LCM of 100 and 85 is 1700
Methods
How to find the LCM of 100 and 85 using Prime Factorization
One way to find the LCM of 100 and 85 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 85?
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 85:
5
1
×
1
7
1
5^1 × 17^1
5 1 × 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, 5, 17
2
2
×
5
2
×
1
7
1
=
1700
2^2 × 5^2 × 17^1 = 1700
2 2 × 5 2 × 1 7 1 = 1700
Through this we see that the LCM of 100 and 85 is 1700.
How to Find the LCM of 100 and 85 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 100 and 85 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 85:
What are the Multiples of 100?
What are the Multiples of 85?
Let’s take a look at the first 10 multiples for each of these numbers, 100 and 85:
First 10 Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850
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 85 are 1700, 3400, 5100. Because 1700 is the smallest, it is the least common multiple.
The LCM of 100 and 85 is 1700.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 10 and 95?
What is the LCM of 57 and 93?
What is the LCM of 27 and 55?
What is the LCM of 23 and 21?
What is the LCM of 31 and 43?