Solution: The LCM of 85 and 146 is 12410
Methods
How to find the LCM of 85 and 146 using Prime Factorization
One way to find the LCM of 85 and 146 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 146?
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 146:
2
1
×
7
3
1
2^1 × 73^1
2 1 × 7 3 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, 73
2
1
×
5
1
×
1
7
1
×
7
3
1
=
12410
2^1 × 5^1 × 17^1 × 73^1 = 12410
2 1 × 5 1 × 1 7 1 × 7 3 1 = 12410
Through this we see that the LCM of 85 and 146 is 12410.
How to Find the LCM of 85 and 146 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 85 and 146 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 146:
What are the Multiples of 85?
What are the Multiples of 146?
Let’s take a look at the first 10 multiples for each of these numbers, 85 and 146:
First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850
First 10 Multiples of 146: 146, 292, 438, 584, 730, 876, 1022, 1168, 1314, 1460
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 146 are 12410, 24820, 37230. Because 12410 is the smallest, it is the least common multiple.
The LCM of 85 and 146 is 12410.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 44 and 138?
What is the LCM of 59 and 4?
What is the LCM of 6 and 61?
What is the LCM of 21 and 46?
What is the LCM of 26 and 15?