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}

Steps to Find the Lowest Common Denominator

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

1. 1. Prime Factor Each Denominator
      Write each prime factor as a power when you have repeating factors.
   2. Write Repeating Factors as Powers
      If a number contains repeated prime factors, rewrite them using exponents.
   3. Multiply the unique prime factors using the highest power of each.
      This product is the lowest common denominator (LCD).

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. Multiply the unique prime factors using the highest power of each.

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

Watch How to Find the LCD

Check out this video where John explains the exact steps on how to find the Lowest Common Denominator or LCD:

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