Solution: The LCM of 67 and 85 is 5695
Methods
How to find the LCM of 67 and 85 using Prime Factorization
One way to find the LCM of 67 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 67?
What are the Factors of 85?
Here is the prime factorization of 67:
6
7
1
67^1
6 7 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: 67, 5, 17
5
1
×
1
7
1
×
6
7
1
=
5695
5^1 × 17^1 × 67^1 = 5695
5 1 × 1 7 1 × 6 7 1 = 5695
Through this we see that the LCM of 67 and 85 is 5695.
How to Find the LCM of 67 and 85 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 67 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, 67 and 85:
What are the Multiples of 67?
What are the Multiples of 85?
Let’s take a look at the first 10 multiples for each of these numbers, 67 and 85:
First 10 Multiples of 67: 67, 134, 201, 268, 335, 402, 469, 536, 603, 670
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 67 and 85 are 5695, 11390, 17085. Because 5695 is the smallest, it is the least common multiple.
The LCM of 67 and 85 is 5695.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 113 and 56?
What is the LCM of 139 and 84?
What is the LCM of 105 and 96?
What is the LCM of 101 and 53?
What is the LCM of 109 and 41?