What Is the Lowest Common Denominator?

What is the lowest common denominator of the pair of fractions 1/2 and 3/4? How about the trio of fractions 1/2, 2/3, and 3/4? What’s the difference between a lowest common denominator and a regular everyday common denominator? And why should you care? Keep on reading to find out!

Jason Marshall, PhD,
December 7, 2012
Episode #132

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In the last episode, I kicked things off by asking you to find the lowest common denominator of a pair of fractions—let’s say 1/2 and 3/4. That question led us down a path in which we discovered the fascinating fact that groups of fractions have not just one but an infinite number of common denominators. And it also led us to discover that calculating lowest common denominators requires that we first know how to calculate least common multiples.

Now that we’ve got all of that stuff figured out and safely secured in our bag of mathematical tricks, we’re ready to move on to the big question: How do you find the lowest common denominator of a pair or a group of fractions? Stay tuned because that’s exactly the problem we’ll be learning to solve today.

Recap: What Is the Least Common Multiple?

If you’re not exactly sure what the least common multiple of a group of numbers is and how to calculate it, I highly recommend taking a look at last week’s show about that very topic before continuing on. Pretty much everything we’re going to do today relies upon that idea, so I promise you it’ll be time well spent. To make sure you’re good-to-go on this topic, here’s a quick question to test yourself: What’s the least common multiple of the numbers 3, 5, and 10? I’ll give you a second to think about it…

So, did you come up with 30? The quick and dirty way to find the least common multiple of a group of numbers is to first figure out what the multiples of each individual number look like. In this case, the multiples of 3 are all the numbers like 3, 6, 9, 12, and so on; the multiples of 5 look like 5, 10, 15, 20, and so on; and the multiples of 10 look like 10, 20, 30, and so on. The least common multiple of a group of numbers is the smallest multiple that all the numbers have in common. Which, in this case, is 30.