Least Common Denominator Calculator

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 and . 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 and is 12, since the LCM(3,4) is 12. Our fractions then become and . We can add, subtract, or compare them to our hearts' content!

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

where:

• — Least common denominator of two fractions;
• — Numerators of the two fractions;
• — Denominators of the two fractions;
• — Least common multiple of the two denominators; and
• — Greatest common factor of the two denominators.

🔎 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:

This may look complex, but it's easier to understand with an example. Let's find the sum of the fractions and :

1. The LCD of and :

2. Rewrite our two fractions in their equivalent forms with the LCD as their denominator:

3. The sum of the fractions and :

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, tick the step-by-step solution checkbox.

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

• LCD calculator;
• Common denominator calculator; and
• Lowest common denominator calculator