Solution: The LCM of 97 and 18 is 1746
Methods
How to find the LCM of 97 and 18 using Prime Factorization
One way to find the LCM of 97 and 18 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 97?
What are the Factors of 18?
Here is the prime factorization of 97:
9
7
1
97^1
9 7 1
And this is the prime factorization of 18:
2
1
×
3
2
2^1 × 3^2
2 1 × 3 2
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: 97, 2, 3
2
1
×
3
2
×
9
7
1
=
1746
2^1 × 3^2 × 97^1 = 1746
2 1 × 3 2 × 9 7 1 = 1746
Through this we see that the LCM of 97 and 18 is 1746.
How to Find the LCM of 97 and 18 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 97 and 18 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, 97 and 18:
What are the Multiples of 97?
What are the Multiples of 18?
Let’s take a look at the first 10 multiples for each of these numbers, 97 and 18:
First 10 Multiples of 97: 97, 194, 291, 388, 485, 582, 679, 776, 873, 970
First 10 Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180
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 97 and 18 are 1746, 3492, 5238. Because 1746 is the smallest, it is the least common multiple.
The LCM of 97 and 18 is 1746.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 107 and 33?
What is the LCM of 61 and 73?
What is the LCM of 43 and 110?
What is the LCM of 103 and 58?
What is the LCM of 111 and 45?