Solution: The LCM of 128 and 97 is 12416
Methods
How to find the LCM of 128 and 97 using Prime Factorization
One way to find the LCM of 128 and 97 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 128?
What are the Factors of 97?
Here is the prime factorization of 128:
2
7
2^7
2 7
And this is the prime factorization of 97:
9
7
1
97^1
9 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: 2, 97
2
7
×
9
7
1
=
12416
2^7 × 97^1 = 12416
2 7 × 9 7 1 = 12416
Through this we see that the LCM of 128 and 97 is 12416.
How to Find the LCM of 128 and 97 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 128 and 97 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, 128 and 97:
What are the Multiples of 128?
What are the Multiples of 97?
Let’s take a look at the first 10 multiples for each of these numbers, 128 and 97:
First 10 Multiples of 128: 128, 256, 384, 512, 640, 768, 896, 1024, 1152, 1280
First 10 Multiples of 97: 97, 194, 291, 388, 485, 582, 679, 776, 873, 970
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 128 and 97 are 12416, 24832, 37248. Because 12416 is the smallest, it is the least common multiple.
The LCM of 128 and 97 is 12416.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 56 and 147?
What is the LCM of 53 and 145?
What is the LCM of 120 and 64?
What is the LCM of 102 and 46?
What is the LCM of 134 and 138?