What is the LCM of 16 and 15?

The LCM, or Least Common Multiple, of two or more numbers is the smallest value that all the numbers considered can be divided into evenly. So, the LCM of 16 and 15 would be the smallest number that can be divided by both 16 and 15 exactly, without any remainder left afterwards.

Solution: The LCM of 16 and 15 is 240

Methods

How to find the LCM of 16 and 15 using Prime Factorization

One way to find the LCM of 16 and 15 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 16:

242^4

And this is the prime factorization of 15:

31×513^1 × 5^1

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, 5

24×31×51=2402^4 × 3^1 × 5^1 = 240

Through this we see that the LCM of 16 and 15 is 240.

How to Find the LCM of 16 and 15 by Listing Common Multiples

The first step to this method of finding the Least Common Multiple of 16 and 15 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, 16 and 15:

What are the Multiples of 16?

What are the Multiples of 15?

Let’s take a look at the first 10 multiples for each of these numbers, 16 and 15:

First 10 Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160

First 10 Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150

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 16 and 15 are 240, 480, 720. Because 240 is the smallest, it is the least common multiple.

The LCM of 16 and 15 is 240.

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