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Common Denominator Calculator

Created by Luis Hoyos
Reviewed by Steven Wooding
Last updated: Jan 18, 2024


If you need to find the common denominator of a set of fractions, this common denominator calculator is the tool you need. You can use it and input up to 5 fractions.

In summary, the least common denominator (LCD) of a set of fractions is the least common multiple (LCM) of its denominators. We usually use it to find equivalent fractions, which are easier to compare, sum, and rest.

To know what are the common denominators and how to find them manually, keep reading this article in which we explain some methods to do it.

How to find the least common denominator

As previously mentioned, finding the least common denominator means just finding the LCM of the denominators.

Below, we present some methods to find the LCM of a set of numbers. To learn more, visit our LCM calculator.

List of multiples

This method consists of finding the multiples of the denominators until encountering the first common multiple. It is convenient when there are small denominators or a few fractions.

For example, suppose you want to find the LCD of 1/3 and 2/7 (which equals 21). There are the steps to find the LCM of the denominators:

  • Obtain the multiples of 7:

    7, 14, 21, 28, 35, 42...

  • And the multiples of 3:

    3, 6, 9, 12, 15, 17, 21, 24, 27, 30, 33, 36, 39, 42...

Prime factorization

Let's look at this method assuming we want to know the least common denominator of 3/4, 4/5, and 2/3. These are the steps:

  1. Decompose the denominators into their prime factors (learn how with our prime factorization calculator):

    4 = 2²
    5 = 5 × 1
    3 = 3 × 1

  2. Find the highest power of each prime number:

    1¹, 2², 3¹, 5¹

  3. Multiply the previous powers:

    1¹ × 2² × 3¹ × 5¹ = 60

Therefore, the answer to what's the least common denominator of 3/4, 4/5, and 2/3 is 60.

Using the greatest common factor (GCF)

If you know the GCF, this is the more straightforward option. The LCM of two numbers (a and b) is the absolute value of their product divided by their GCF:

LCD(a,b) = |a × b|/GCF(a, b)

For more than two numbers, we take the LCM of the first two numbers and use it alongside the third number to obtain the final LCM. For example, the LCM of a, b, and c equals the LCM of LCM(a, b) and c:

LCM(a,b,c) = LCM(LCM(a,b), c)

The process repeats and repeats as we face more numbers:
LCM(a,b,c,d) = LCM(LCM(a,b,c),d)

Learn how to find the greatest common factor with our GCF calculator.

What are the common denominators?

Let's remember the list of multiples from the previous section:

  • Multiples of 7:

    7, 14, 21, 28, 35, 42...

  • Multiples of 3:

    3, 6, 9, 12, 15, 17, 21, 24, 27, 30, 33, 36, 39, 42...

Above, you can see the number 42 is present in both lists, which means it is a common denominator. Common denominators are infinite, and you keep finding them forever. On the other side, the least common denominator is only one. In this case, 42 is a common denominator but not the least common denominator.

Other common denominator calculators

Now that you know how to find common denominators and their least value, take a look at these similar tools:

FAQ

How do I find the LCD of 1/3 and 2/7?

To find the LCD of 1/3 and 2/7:

  1. Identify the denominators: 3 and 7.

  2. Find the least common multiple (LCM) of the denominators:

    • Multiples of 7:

      7, 14, 21, 28, 35, 42...

    • Multiples of 3:

      3, 6, 9, 12, 15, 17, 21, 24, 27.

  3. Therefore, the LCD of 1/2 and 2/7 is 21, which is the LCM of 3 and 7 (the denominators).

What is the least common denominator of 2/3 and 5/8?

24. To know what is the least common denominator of 2/3 and 5/8:

  1. Find the least common multiple (LCM) of the denominators (3 and 8):

    • Multiples of 8:

      8, 16, 24, 32, 40, 48...

    • Multiples of 3:

      3, 6, 9, 12, 15, 17, 21, 24, 27, 30...

  2. The LCM of 3 and 8 is 24. Therefore, the LCD of 2/3 and 5/8 is 24, as the LCD of two fractions is the LCM of their denominators.

What's the least common denominator of 3/4, 4/5, and 2/3?

60. To know the least common denominator of 3/4, 4/5, and 2/3, find the least common multiple of the denominators, which is LCM(4,5,3) = 60 in this case.

Luis Hoyos
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Common denominator results
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