Least Common Denominator Calculator

Created by Krishna Nelaturu
Reviewed by Luis Hoyos
Last updated: Mar 22, 2023


You can use our least common denominator calculator to find the least common denominator of a set of fractions so that you can easily perform arithmetic operations on fractions like addition or subtraction. It can handle both simple and mixed fractions!

Want to know how to find the least common denominator? In the following article, we shall walk you through some fundamentals, such as:

  • What is the least common denominator?
  • Calculating the least common denominator for fractions.
  • Relation between least common denominator, least common multiple, and greatest common factor.

What is the least common denominator?

The least common denominator (LCD) is the least common multiple (LCM) of all the denominators in a given set of fractions.

For example, consider the fractions 23\frac{2}{3} and 34\frac{3}{4}. At one glance, we cannot tell which is the largest or the smallest because comparisons (and arithmetic operations) on fractions are only valid if they share the same denominator. To make this happen, let's find their LCD.

The least common denominator of 23\frac{2}{3} and 34\frac{3}{4} is 12, since the LCM(3,4) is 12. Our fractions then become 812\frac{8}{12} and 912\frac{9}{12}. We can add, subtract, or compare them to our hearts' content!

How to find the least common denominator?

Finding the least common denominator requires us to calculate the least common multiple of the denominators.

LCD(ab,cd)=LCM(b,d)=bβ‹…dGCF(b,d)LCD\left(\frac{a}{b}, \frac{c}{d}\right) = LCM(b,d) = \frac{b \cdot d}{GCF(b,d)}

Where:

  • LCDLCD - Least common denominator of two fractions;
  • a,ca, c - Numerators of the two fractions;
  • b,db, d - Denominators of the two fractions;
  • LCMLCM - Least common multiple of the two denominators; and
  • GCFGCF - Greatest common factor of the two denominators.

πŸ”Ž You can learn about LCM and GCF calculation with our GCF calculator and LCM calculator.

After finding LCD, we must calculate equivalent fractions of the original fractions such that their denominators are equal to the LCD. We can achieve this by:

ab=abΓ—dGCF(b,d)dGCF(b,d)=aβ‹…dGCF(b,d)bβ‹…dGCF(b,d)cd=cdΓ—bGCF(b,d)bGCF(b,d)=cβ‹…bGCF(b,d)dβ‹…bGCF(b,d)\frac{a}{b} = \frac{a}{b} \times \frac{\frac{d}{GCF(b,d)}}{\frac{d}{GCF(b,d)}} =\frac{\frac{a \cdot d}{GCF(b,d)}}{\frac{b \cdot d}{GCF(b,d)}} \\[1em] \frac{c}{d} = \frac{c}{d} \times \frac{\frac{b}{GCF(b,d)}}{\frac{b}{GCF(b,d)}} = \frac{\frac{c \cdot b}{GCF(b,d)}}{\frac{d \cdot b}{GCF(b,d)}}\\

This may look complex, but it's easier to understand with an example. Let's find the sum of the fractions 38\frac{3}{8} and 512\frac{5}{12}:

  1. The LCD of 38\frac{3}{8} and 512\frac{5}{12}:
LCD(38,512)=LCM(8,12)=8β‹…12GCF(8,12)=8β‹…124=8β‹…3LCD(38,512)=24\small \qquad \begin{align*} LCD\left(\frac{3}{8}, \frac{5}{12}\right) &= LCM(8,12)\\ &= \frac{8 \cdot 12}{GCF(8,12)}\\[1em] &= \frac{8 \cdot 12}{4} = 8 \cdot 3\\ LCD\left(\frac{3}{8}, \frac{5}{12}\right) &= 24 \end{align*}
  1. Rewrite our two fractions in their equivalent forms with the LCD as their denominator:
38=38Γ—12GCF(8,12)12GCF(8,12)=38Γ—124124=3β‹…38β‹…338=924512=512Γ—8GCF(8,12)8GCF(8,12)=512Γ—8484=5β‹…212β‹…2512=1024\small \qquad \begin{align*} \frac{3}{8} &= \frac{3}{8} \times \frac{\frac{12}{GCF(8,12)}}{\frac{12}{GCF(8,12)}}\\[1em] &= \frac{3}{8} \times \frac{\frac{12}{4}}{\frac{12}{4}} = \frac{3 \cdot 3}{8 \cdot 3}\\[1em] \frac{3}{8}&= \frac{9}{24}\\[1em] \frac{5}{12} &= \frac{5}{12} \times \frac{\frac{8}{GCF(8,12)}}{\frac{8}{GCF(8,12)}}\\[1em] &= \frac{5}{12} \times \frac{\frac{8}{4}}{\frac{8}{4}} = \frac{5 \cdot 2}{12 \cdot 2}\\[1em] \frac{5}{12}&= \frac{10}{24} \end{align*}
  1. The sum of the fractions 38\frac{3}{8} and 512\frac{5}{12}:
38+512=924+1024=9+1024=1924\small \qquad \begin{align*} \frac{3}{8} + \frac{5}{12} = \frac{9}{24} + \frac{10}{24} = \frac{9+10}{24} = \frac{19}{24} \end{align*}

Using this calculator to find the least common denominator

Our least common denominator calculator is simple to use:

  1. Select the type of fraction. You can choose between:
    • Simple fraction; and
    • Mixed fraction.
  2. For simple fractions, enter the numerators and denominators of each fraction. You can enter up to five fractions in our LCD calculator.
  3. For mixed fractions, enter the whole numbers, numerators, and denominators of each fraction.
  4. Our calculator shall find the least common denominator along with the rewritten forms of the original fractions.
  5. If you wish to verify the calculation steps, choose yes in the step-by-step solution field.

Similar tools

If you liked our least common denominator calculator, here are some other tools that are based on the same concept:

FAQ

What is the least common denominator of 1/4 and 1/6?

For two fractions whose denominators are 4 and 6, the least common denominator is 12. The following steps will help you reach the same answer:

  1. List all common multiples of the denominators 4 and 6.
    • 4: 4, 8, 12, 16, 20, 24, 28,...
    • 6: 6, 12, 18, 24, 30, 36,...
  2. The least common multiple of 4 and 6 is 12.
  3. The least common denominator of 1/4 and 1/6 is 12.
  4. Verify your result with our least common denominator calculator.

Do you need to find the least common denominator for multiplying fractions?

No. Adding or subtracting fractions requires the fractions to have the same denominator, whereas multiplying or dividing fractions has no such requirement. So you can multiply or divide fractions with different denominators.

Krishna Nelaturu
Fraction form
Simple fraction
Values (enter up to 5 fractions)
1st fraction
Numerator (n₁)
Denominator (d₁)
2nd fraction
Numerator (nβ‚‚)
Denominator (dβ‚‚)
Least Common Denominator
Step by step solution?
No
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