Solution: The LCM of 85 and 123 is 10455
Methods
How to find the LCM of 85 and 123 using Prime Factorization
One way to find the LCM of 85 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 85?
What are the Factors of 123?
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 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: 5, 17, 3, 41
3
1
×
5
1
×
1
7
1
×
4
1
1
=
10455
3^1 × 5^1 × 17^1 × 41^1 = 10455
3 1 × 5 1 × 1 7 1 × 4 1 1 = 10455
Through this we see that the LCM of 85 and 123 is 10455.
How to Find the LCM of 85 and 123 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 85 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, 85 and 123:
What are the Multiples of 85?
What are the Multiples of 123?
Let’s take a look at the first 10 multiples for each of these numbers, 85 and 123:
First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850
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 85 and 123 are 10455, 20910, 31365. Because 10455 is the smallest, it is the least common multiple.
The LCM of 85 and 123 is 10455.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 43 and 137?
What is the LCM of 9 and 49?
What is the LCM of 76 and 61?
What is the LCM of 2 and 52?
What is the LCM of 147 and 125?