Solution: The LCM of 112 and 128 is 896
Methods
How to find the LCM of 112 and 128 using Prime Factorization
One way to find the LCM of 112 and 128 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 112?
What are the Factors of 128?
Here is the prime factorization of 112:
2
4
×
7
1
2^4 × 7^1
2 4 × 7 1
And this is the prime factorization of 128:
2
7
2^7
2 7
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, 7
2
7
×
7
1
=
896
2^7 × 7^1 = 896
2 7 × 7 1 = 896
Through this we see that the LCM of 112 and 128 is 896.
How to Find the LCM of 112 and 128 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 112 and 128 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, 112 and 128:
What are the Multiples of 112?
What are the Multiples of 128?
Let’s take a look at the first 10 multiples for each of these numbers, 112 and 128:
First 10 Multiples of 112: 112, 224, 336, 448, 560, 672, 784, 896, 1008, 1120
First 10 Multiples of 128: 128, 256, 384, 512, 640, 768, 896, 1024, 1152, 1280
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 112 and 128 are 896, 1792, 2688. Because 896 is the smallest, it is the least common multiple.
The LCM of 112 and 128 is 896.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 31 and 113?
What is the LCM of 107 and 77?
What is the LCM of 150 and 132?
What is the LCM of 100 and 99?
What is the LCM of 105 and 6?