What is the LCM of 119 and 106?

One way to find the LCM of 119 and 106 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 106?

Here is the prime factorization of 119:

And this is the prime factorization of 106:

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, 2, 53

Through this we see that the LCM of 119 and 106 is 12614.

The first step to this method of finding the Least Common Multiple of 119 and 106 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 106:

What are the Multiples of 119?

What are the Multiples of 106?

Let’s take a look at the first 10 multiples for each of these numbers, 119 and 106:

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

First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060

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 106 are 12614, 25228, 37842. Because 12614 is the smallest, it is the least common multiple.

The LCM of 119 and 106 is 12614.

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

• What is the LCM of 53 and 105?
• What is the LCM of 101 and 2?
• What is the LCM of 100 and 112?
• What is the LCM of 69 and 137?
• What is the LCM of 14 and 148?