Solution: The LCM of 56 and 126 is 504
Methods
How to find the LCM of 56 and 126 using Prime Factorization
One way to find the LCM of 56 and 126 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 56?
What are the Factors of 126?
Here is the prime factorization of 56:
2
3
×
7
1
2^3 × 7^1
2 3 × 7 1
And this is the prime factorization of 126:
2
1
×
3
2
×
7
1
2^1 × 3^2 × 7^1
2 1 × 3 2 × 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, 7, 3
2
3
×
3
2
×
7
1
=
504
2^3 × 3^2 × 7^1 = 504
2 3 × 3 2 × 7 1 = 504
Through this we see that the LCM of 56 and 126 is 504.
How to Find the LCM of 56 and 126 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 56 and 126 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, 56 and 126:
What are the Multiples of 56?
What are the Multiples of 126?
Let’s take a look at the first 10 multiples for each of these numbers, 56 and 126:
First 10 Multiples of 56: 56, 112, 168, 224, 280, 336, 392, 448, 504, 560
First 10 Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260
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 56 and 126 are 504, 1008, 1512. Because 504 is the smallest, it is the least common multiple.
The LCM of 56 and 126 is 504.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 15 and 147?
What is the LCM of 80 and 148?
What is the LCM of 107 and 122?
What is the LCM of 84 and 111?
What is the LCM of 42 and 126?