Solution: The LCM of 7 and 89 is 623
Methods
How to find the LCM of 7 and 89 using Prime Factorization
One way to find the LCM of 7 and 89 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 7?
What are the Factors of 89?
Here is the prime factorization of 7:
7
1
7^1
7 1
And this is the prime factorization of 89:
8
9
1
89^1
8 9 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: 7, 89
7
1
×
8
9
1
=
623
7^1 × 89^1 = 623
7 1 × 8 9 1 = 623
Through this we see that the LCM of 7 and 89 is 623.
How to Find the LCM of 7 and 89 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 7 and 89 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, 7 and 89:
What are the Multiples of 7?
What are the Multiples of 89?
Let’s take a look at the first 10 multiples for each of these numbers, 7 and 89:
First 10 Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
First 10 Multiples of 89: 89, 178, 267, 356, 445, 534, 623, 712, 801, 890
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 7 and 89 are 623, 1246, 1869. Because 623 is the smallest, it is the least common multiple.
The LCM of 7 and 89 is 623.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 27 and 138?
What is the LCM of 68 and 118?
What is the LCM of 71 and 56?
What is the LCM of 47 and 77?
What is the LCM of 90 and 11?