Solution: The LCM of 85 and 16 is 1360
Methods
How to find the LCM of 85 and 16 using Prime Factorization
One way to find the LCM of 85 and 16 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 16?
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 16:
2
4
2^4
2 4
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
2
4
×
5
1
×
1
7
1
=
1360
2^4 × 5^1 × 17^1 = 1360
2 4 × 5 1 × 1 7 1 = 1360
Through this we see that the LCM of 85 and 16 is 1360.
How to Find the LCM of 85 and 16 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 85 and 16 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 16:
What are the Multiples of 85?
What are the Multiples of 16?
Let’s take a look at the first 10 multiples for each of these numbers, 85 and 16:
First 10 Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850
First 10 Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160
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 16 are 1360, 2720, 4080. Because 1360 is the smallest, it is the least common multiple.
The LCM of 85 and 16 is 1360.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 149 and 18?
What is the LCM of 107 and 52?
What is the LCM of 8 and 40?
What is the LCM of 84 and 140?
What is the LCM of 58 and 37?