Solution: The LCM of 51 and 56 is 2856
Methods
How to find the LCM of 51 and 56 using Prime Factorization
One way to find the LCM of 51 and 56 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 51?
What are the Factors of 56?
Here is the prime factorization of 51:
3
1
×
1
7
1
3^1 × 17^1
3 1 × 1 7 1
And this is the prime factorization of 56:
2
3
×
7
1
2^3 × 7^1
2 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: 3, 17, 2, 7
2
3
×
3
1
×
7
1
×
1
7
1
=
2856
2^3 × 3^1 × 7^1 × 17^1 = 2856
2 3 × 3 1 × 7 1 × 1 7 1 = 2856
Through this we see that the LCM of 51 and 56 is 2856.
How to Find the LCM of 51 and 56 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 51 and 56 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, 51 and 56:
What are the Multiples of 51?
What are the Multiples of 56?
Let’s take a look at the first 10 multiples for each of these numbers, 51 and 56:
First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510
First 10 Multiples of 56: 56, 112, 168, 224, 280, 336, 392, 448, 504, 560
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 51 and 56 are 2856, 5712, 8568. Because 2856 is the smallest, it is the least common multiple.
The LCM of 51 and 56 is 2856.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 102 and 106?
What is the LCM of 136 and 29?
What is the LCM of 8 and 52?
What is the LCM of 133 and 24?
What is the LCM of 100 and 57?