Solution: The LCM of 105 and 128 is 13440
Methods
How to find the LCM of 105 and 128 using Prime Factorization
One way to find the LCM of 105 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 105?
What are the Factors of 128?
Here is the prime factorization of 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 5 1 × 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: 3, 5, 7, 2
2
7
×
3
1
×
5
1
×
7
1
=
13440
2^7 × 3^1 × 5^1 × 7^1 = 13440
2 7 × 3 1 × 5 1 × 7 1 = 13440
Through this we see that the LCM of 105 and 128 is 13440.
How to Find the LCM of 105 and 128 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 105 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, 105 and 128:
What are the Multiples of 105?
What are the Multiples of 128?
Let’s take a look at the first 10 multiples for each of these numbers, 105 and 128:
First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050
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 105 and 128 are 13440, 26880, 40320. Because 13440 is the smallest, it is the least common multiple.
The LCM of 105 and 128 is 13440.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 69 and 110?
What is the LCM of 66 and 33?
What is the LCM of 79 and 129?
What is the LCM of 126 and 96?
What is the LCM of 51 and 34?