Solution: The LCM of 126 and 19 is 2394
Methods
How to find the LCM of 126 and 19 using Prime Factorization
One way to find the LCM of 126 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 126?
What are the Factors of 19?
Here is the prime factorization of 126:
2
1
×
3
2
×
7
1
2^1 × 3^2 × 7^1
2 1 × 3 2 × 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, 3, 7, 19
2
1
×
3
2
×
7
1
×
1
9
1
=
2394
2^1 × 3^2 × 7^1 × 19^1 = 2394
2 1 × 3 2 × 7 1 × 1 9 1 = 2394
Through this we see that the LCM of 126 and 19 is 2394.
How to Find the LCM of 126 and 19 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 126 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, 126 and 19:
What are the Multiples of 126?
What are the Multiples of 19?
Let’s take a look at the first 10 multiples for each of these numbers, 126 and 19:
First 10 Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260
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 126 and 19 are 2394, 4788, 7182. Because 2394 is the smallest, it is the least common multiple.
The LCM of 126 and 19 is 2394.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 36 and 64?
What is the LCM of 137 and 71?
What is the LCM of 98 and 52?
What is the LCM of 132 and 120?
What is the LCM of 62 and 58?