Solution: The LCM of 85 and 124 is 10540
Methods
How to find the LCM of 85 and 124 using Prime Factorization
One way to find the LCM of 85 and 124 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 85?
What are the Factors of 124?
Here is the prime factorization of 85:
5
1
×
1
7
1
5^1 × 17^1
5 1 × 1 7 1
And this is the prime factorization of 124:
2
2
×
3
1
1
2^2 × 31^1
2 2 × 3 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: 5, 17, 2, 31
2
2
×
5
1
×
1
7
1
×
3
1
1
=
10540
2^2 × 5^1 × 17^1 × 31^1 = 10540
2 2 × 5 1 × 1 7 1 × 3 1 1 = 10540
Through this we see that the LCM of 85 and 124 is 10540.
How to Find the LCM of 85 and 124 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 85 and 124 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, 85 and 124:
What are the Multiples of 85?
What are the Multiples of 124?
Let’s take a look at the first 10 multiples for each of these numbers, 85 and 124:
First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850
First 10 Multiples of 124: 124, 248, 372, 496, 620, 744, 868, 992, 1116, 1240
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 85 and 124 are 10540, 21080, 31620. Because 10540 is the smallest, it is the least common multiple.
The LCM of 85 and 124 is 10540.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 23 and 129?
What is the LCM of 2 and 126?
What is the LCM of 122 and 128?
What is the LCM of 8 and 79?
What is the LCM of 111 and 68?