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Lowest Common Denominator Calculator (LCD)

Written by:
PK

On this page is a least or lowest common denominator calculator. Enter fractions or positive integers, and the tool will return the lowest common denominator (LCD) of each term and list the new form of each number in the results.

Looking for another close tool? Try one of these instead:

Lowest Common Denominator (LCD) Calculator

What is the Least or Lowest Common Denominator (LCD)?

The least or lowest common denominator (LCD) is the smallest number which is a multiple of every denominator in the set. Expressing each fraction or number in a set in terms of a common denominator simplifies math on those numbers.

The lowest common denominator is sometimes – but not always – the product of every denominator. Other times, it is one of the denominators already in the set.

Finding the Lowest Common Denominator

Let's find the LCD – using a brute force multiplication method – for the 4 numbers included in the tool: 2/3, 10, 12/5, and 4.

(Note that we can rewrite the integers as fractions over '1': 2/3, 10/1, 12/5, and 4/1.)

Strip the denominators out and multiply:

3*1*5*1=15

Now, rewrite each fraction with a denominator of 15. (Multiplying the numerator and denominator by the same amount):

\frac{2}{3}=\frac{10}{15}\\\frac{10}{1}=\frac{150}{15}\\\frac{12}{5}=\frac{36}{15}\\\frac{4}{1}=\frac{60}{15}

At this point, you can now reduce each fraction by finding common factors. However, you can't here – 36, 10, 150, and 60 share no factors other than 1.

Using the Lowest Common Denominator Calculator

In the text box, enter your list of numbers to find the lowest common factor. You can enter whole numbers, fractions (using '/'), negatives, and decimals – but fractions and positive numbers make the most sense.

Next, press the Compute LCD button. We'll return the Lowest Common Denominator and the total count of numbers we understood..

Enjoyed this? Visit our other calculators and tools. Also see our factor calculator and prime factorization calculator.

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