Solution: The LCM of 85 and 104 is 8840
Methods
How to find the LCM of 85 and 104 using Prime Factorization
One way to find the LCM of 85 and 104 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 104?
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 104:
2
3
×
1
3
1
2^3 × 13^1
2 3 × 1 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, 13
2
3
×
5
1
×
1
3
1
×
1
7
1
=
8840
2^3 × 5^1 × 13^1 × 17^1 = 8840
2 3 × 5 1 × 1 3 1 × 1 7 1 = 8840
Through this we see that the LCM of 85 and 104 is 8840.
How to Find the LCM of 85 and 104 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 85 and 104 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 104:
What are the Multiples of 85?
What are the Multiples of 104?
Let’s take a look at the first 10 multiples for each of these numbers, 85 and 104:
First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850
First 10 Multiples of 104: 104, 208, 312, 416, 520, 624, 728, 832, 936, 1040
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 104 are 8840, 17680, 26520. Because 8840 is the smallest, it is the least common multiple.
The LCM of 85 and 104 is 8840.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 8 and 63?
What is the LCM of 111 and 116?
What is the LCM of 72 and 60?
What is the LCM of 68 and 43?
What is the LCM of 35 and 77?