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Math Fractions – How to Find the Lowest Common Denominator

By Stuart Ackerman

Part 1

Finding the common denominator is an important fractions skill for students in grades 4-6.

Here is how you can help your child find the common denominator:

Let’s assume you have 2/3 of a bag of marbles and your friend has 3/4 of a bag as well. You are trying to figure out if you have a whole bag together.

What you want to do here is add 2/3 and 3/4 of the bags of marbles.

We cannot add 2/3 and 3/4 because they have different denominators (the bottom number of a fraction), so, we have to make the denominators the same. This is a common denominator.

One of the easiest ways to find a common denominator is to multiply the two denominators together. So we would multiply 3 x 4 = 12.

Now, let’s take our first fraction of 2/3. What did we multiply the denominator (3) by in order to get 12? We multiplied it by 4. So we do the same for the top, 2 x 4 = 8. Now we have a new fraction, 8/12.

Let’s take the second fraction, 3/4 and do the same. What did we multiply the denominator (4) by in order to get 12? We multiplied by 3, so we’ll do the same for the numerator, 3 x 3 = 9. Now we have our second new fraction, 9/12.

Finally, we can add the two fractions 8/12 + 9/12 = 17/12 or 1 and 5/12. This answers our question. We have over 1 full bag of marbles.

Now, let’s assume that we started off with a different fraction and our answer was something like 7/9. Here, we wouldn’t quite have 1 whole bag; instead, we would have a fraction of a bag (i.e. 7/9).

Part 2

Let’s take two other fractions this time. Let’s try to add 4/6 and 1/4. In the first example, we multiplied the denominators in order to find the common denominator.

This time we’ll do something a little different.

First, we will find the multiples of the denominators. For example:

In the fraction 4/6, 6 is the denominator.

Here are the multiples of 6:

6, 12, 18, 24

Let’s do the same for 1/4:

Here are the multiples of 4:

4, 8, 12, 16, 20, 24

Now, if we had just multiplied the denominators in this example as we did in Part1, we would have had 6 x 4 = 24.

But,

24 is NOT the lowest common denominator!

Let’s look at the multiples of 6 and 4 and find the lowest common denominator:

4: 4, 8, 12, 16, 20, 24

6: 6, 12, 18, 24

Notice how 12 is the lowest common denominator! This is an easier method than if we had multiplied the denominators and had to reduce the fraction to get a common denominator. Now we would go through the same steps as in Part 1 by changing the numerators and adding.

Now you have a better understanding of how to find the lowest common denominator by first writing down the multiples of the two denominators, finding the lowest common multiple, and plugging it in as the lowest common denominator.

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See some of the lessons in our video library.

FACTORS - Lesson (A) Introduction to Factors (Grade 7)
FACTORS - Lesson (B) Prime Factorization (Grades 7-8)
FRACTIONS - Lesson (A) Introduction to Fractions (Grades 1-2)

FRACTIONS - Lesson (B) Fractions of Sets (Grade 3)

FRACTIONS - Lesson (C) Comparing Fractions (Grade 3)

FRACTIONS - Lesson (D) Equivalent (Grades 4-5)

FRACTIONS - Lesson (E) Equivalent (Numerical) (Grades 4-5)

FRACTIONS - Lesson (F) Changing Fractions to Decimals (Grades 4-5)

FRACTIONS - Lesson (F2) Changing Fractions to Decimals Using Division (Grades 5-6)

FRACTIONS - Lesson (G) Changing Decimals into Fractions (Grades 4-6)

FRACTIONS - Lesson (H) Comparing (Grade 5)