What is the LCM of 19 and 51?

Solution: The LCM of 19 and 51 is 969

Methods

How to find the LCM of 19 and 51 using Prime Factorization

One way to find the LCM of 19 and 51 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:

Here is the prime factorization of 19:

19^1

And this is the prime factorization of 51:

3^1 × 17^1

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: 19, 3, 17

3^1 × 17^1 × 19^1 = 969

Through this we see that the LCM of 19 and 51 is 969.

How to Find the LCM of 19 and 51 by Listing Common Multiples

The first step to this method of finding the Least Common Multiple of 19 and 51 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, 19 and 51:

What are the Multiples of 19?

What are the Multiples of 51?

Let’s take a look at the first 10 multiples for each of these numbers, 19 and 51:

First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190

First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510

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 19 and 51 are 969, 1938, 2907. Because 969 is the smallest, it is the least common multiple.

The LCM of 19 and 51 is 969.

Find the LCM of Other Number Pairs

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

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