How to Find the Lowest Common Denominator (LCD)

Here’s a quick tutorial on how to find the Lowest Common Denominator also known as Least Common Denominator, or LCD.

 

When you want to add or subtract fractions the denominators need to be the same. For example, you can add  \large \frac{1}{5}+\frac{2}{5}  because the denominators are “common” or the same – all we need to do is add the respective numerators to get the answer, in this case it’s \large \frac{3}{5} .

 

However, in fraction problems where the denominators are not the same like \large \frac{3}{20}+\frac{1}{24}  we need to find the LCD or lowest common denominator so we can rewrite each fraction with common denominators.

 

Note: if you have mixed number fractions, write them as improper fractions before starting these steps. For example…
\large  3\frac{1}{2}=\frac{7}{2}

Now let’s explore the steps on how to find the LCD.

1. Prime Factor Each Denominator
2. Write each prime factor as a power when you have repeating factors.
3. LCD = product of each unique prime factor; only need to have the highest power of powers with the same base.

 

Here is a basic example:

Find the LCD for \large \frac{3}{20}+\frac{1}{24}

 

1. Prime Factor Each Denominator

Prime factors of 20 = 4 x 5 or 2 x 2 x 5

Prime factors of 24 = 8 x 3 or 2 x 2 x 2 x 3

 

2. Write each prime factor as a power when you have repeating factors.

Prime factors of 20 = 2 x 2 x 5 = 2^2 x 5

Prime factors of 24 = 2 x 2 x 2 x 3 = 2^3 x 3

• • • 2^3 is the highest power of 2 so this is what we need to use in the LCD.

3. LCD = product of each unique prime factors; only need to have the highest power with powers with the same base.

LCD = 2^3 x 3 x 5 = 8 x 3 x 5 = 120

 

Check out this video to watch the exact steps on how to find the Lowest Common Denominator or LCD in action:

 

Need more help with fractions? Check out our full Pre-Algebra or Math Foundations course to learn much, much more!