MATH SOLVE

3 months ago

Q:
# What is the LCM of 128 and 37?

Accepted Solution

A:

Solution: The LCM of 128 and 37 is 4736
Methods
How to find the LCM of 128 and 37 using Prime Factorization
One way to find the LCM of 128 and 37 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 37?
Here is the prime factorization of 128:
2
7
2^7
2 7
And this is the prime factorization of 37:
3
7
1
37^1
3 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, 37
2
7
×
3
7
1
=
4736
2^7 × 37^1 = 4736
2 7 × 3 7 1 = 4736
Through this we see that the LCM of 128 and 37 is 4736.
How to Find the LCM of 128 and 37 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 128 and 37 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 37:
What are the Multiples of 128?
What are the Multiples of 37?
Let’s take a look at the first 10 multiples for each of these numbers, 128 and 37:
First 10 Multiples of 128: 128, 256, 384, 512, 640, 768, 896, 1024, 1152, 1280
First 10 Multiples of 37: 37, 74, 111, 148, 185, 222, 259, 296, 333, 370
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 37 are 4736, 9472, 14208. Because 4736 is the smallest, it is the least common multiple.
The LCM of 128 and 37 is 4736.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 54 and 24?
What is the LCM of 53 and 32?
What is the LCM of 134 and 104?
What is the LCM of 37 and 122?
What is the LCM of 114 and 79?