What is the LCM of 119 and 19?

One way to find the LCM of 119 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 119?
• What are the Factors of 19?

Here is the prime factorization of 119:

And this is the prime factorization of 19:

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: 7, 17, 19

Through this we see that the LCM of 119 and 19 is 2261.

The first step to this method of finding the Least Common Multiple of 119 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, 119 and 19:

What are the Multiples of 119?

What are the Multiples of 19?

Let’s take a look at the first 10 multiples for each of these numbers, 119 and 19:

First 10 Multiples of 119: 119, 238, 357, 476, 595, 714, 833, 952, 1071, 1190

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 119 and 19 are 2261, 4522, 6783. Because 2261 is the smallest, it is the least common multiple.

The LCM of 119 and 19 is 2261.

Want more practice? Try some of these other LCM problems:

• What is the LCM of 78 and 76?
• What is the LCM of 89 and 138?
• What is the LCM of 83 and 30?
• What is the LCM of 58 and 22?
• What is the LCM of 114 and 113?