Solution: The LCM of 56 and 19 is 1064
Methods
How to find the LCM of 56 and 19 using Prime Factorization
One way to find the LCM of 56 and 19 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 19?
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 19:
1
9
1
19^1
1 9 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, 19
2
3
×
7
1
×
1
9
1
=
1064
2^3 × 7^1 × 19^1 = 1064
2 3 × 7 1 × 1 9 1 = 1064
Through this we see that the LCM of 56 and 19 is 1064.
How to Find the LCM of 56 and 19 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 56 and 19 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 19:
What are the Multiples of 56?
What are the Multiples of 19?
Let’s take a look at the first 10 multiples for each of these numbers, 56 and 19:
First 10 Multiples of 56: 56, 112, 168, 224, 280, 336, 392, 448, 504, 560
First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190
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 19 are 1064, 2128, 3192. Because 1064 is the smallest, it is the least common multiple.
The LCM of 56 and 19 is 1064.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 107 and 12?
What is the LCM of 10 and 63?
What is the LCM of 92 and 73?
What is the LCM of 147 and 18?
What is the LCM of 119 and 62?