Solution: The LCM of 123 and 85 is 10455
Methods
How to find the LCM of 123 and 85 using Prime Factorization
One way to find the LCM of 123 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 123?
What are the Factors of 85?
Here is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 1 1
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: 3, 41, 5, 17
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 123 and 85 is 10455.
How to Find the LCM of 123 and 85 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 123 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, 123 and 85:
What are the Multiples of 123?
What are the Multiples of 85?
Let’s take a look at the first 10 multiples for each of these numbers, 123 and 85:
First 10 Multiples of 123: 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230
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 123 and 85 are 10455, 20910, 31365. Because 10455 is the smallest, it is the least common multiple.
The LCM of 123 and 85 is 10455.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 98 and 42?
What is the LCM of 22 and 132?
What is the LCM of 138 and 146?
What is the LCM of 17 and 141?
What is the LCM of 27 and 69?