How to Find Least Common Denominators

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  • 0:10 What Is a Multiple?
  • 0:30 Finding an LCD Using Multiples
  • 1:44 Example
  • 2:59 Example 2
  • 4:00 Lesson Summary
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Instructor: Chad Sorrells

Chad has taught Math for the last 9 years in Middle School. He has an M.S. in Instructional Technology and Elementary Education.

Finding a Least Common Denominator is an important tool when working with fractions. To find least common denominators, we will use multiples of our numbers.

What is a Multiple?

When finding the least common denominator, we will be using multiples. Multiples are the products of a given number. For example, the multiples of 2 would be 2, 4, 6, 8, 10, etc… We often call the least common denominator the least common multiple or the LCM.

Finding a Least Common Denominator Using Multiples

Using these multiples, we can now find a common denominator. The least common denominator is the smallest common multiple of both denominators. To begin, let's look at two fractions, 2/4 and 6/9.

We can see that our denominators are 4 and 9. The first thing we need to do is to list out several multiples of each number. A good amount to start with is 10 of each.

The first 10 multiples of 4 are

4, 8, 12, 16, 20, 24, 28, 32, 36, and 40.

The first 10 multiples of 9 are

9, 18, 27, 36, 45, 54, 63, 72, 81, and 90.

Starting with the multiples of the smallest number, 4, we are looking to see if there is a common multiple within the multiples of 9. We can see that both 4 and 9 have the multiple of 36.

Since 36 is the smallest common multiple, it is called our least common multiple, or LCM; so the LCM of 4 and 9 is 36.


Jerry and Tom both collect baseball cards. Jerry puts his cards into pages that contain 16 cards each, and Tom puts his cards into pages that contain 12 cards each. Both Jerry and Tom are curious about how many full pages of cards that they will need to have the same number of cards.

Jerry and Tom know that they must find the least common denominator to see at what number they will have the same number of cards. To begin, Jerry lists the first 10 multiples of 16, which are 16, 32, 48, 64, 80, 96, 112, 128, 144, and 160. Next, Tom lists the first 10 multiples of 12, which are 12, 24, 36, 48, 60, 72, 84, 96, 108, and 120.

Tom and Jerry can see that both of their sets contain the numbers 48 and 96. Since 48 is the smallest number, it is called the least common denominator.

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