Common Denominator Calculator
Enter two fractions to find their least common denominator and rewrite both over it.
The least common denominator (LCD) of two fractions is the least common multiple of their denominators. Find it by dividing the product of the denominators by their greatest common divisor. Then rewrite each fraction with the LCD by multiplying its top and bottom by the same factor, and the fractions can be compared or added.
How to Use This Calculator
Enter the top and bottom of each fraction. The calculator finds the least common denominator, rewrites both fractions over it, and shows their sum. It works with any whole-number denominators.
A common denominator is what you need before you can add, subtract or directly compare two fractions, because fractions can only be combined when they are split into the same-sized pieces.
How the Calculation Works
The least common denominator is the least common multiple of the two denominators. The quickest way to find it is to multiply the denominators together and divide by their greatest common divisor, which removes the overlap that would otherwise make the denominator larger than necessary.
Once the LCD is known, each fraction is rewritten by multiplying its numerator and denominator by whatever turns its denominator into the LCD. That keeps each fraction's value the same while giving both the same denominator.
LCD = (d₁ × d₂) ÷ GCD(d₁, d₂)
Worked Example
Take 1/4 and 1/6. The greatest common divisor of 4 and 6 is 2, so the LCD is (4 × 6) ÷ 2 = 12.
Rewrite each: 1/4 = 3/12 (multiply by 3/3) and 1/6 = 2/12 (multiply by 2/2). Now they add easily: 3/12 + 2/12 = 5/12.
Assumptions and Limitations
- Works with two fractions that have whole-number denominators
- Uses the least common denominator, not just the product of denominators
- The sum shown is not automatically reduced to lowest terms
- Denominators cannot be zero
Who Uses a Common Denominator Calculator
Students, parents helping with homework, and teachers use this to find the least common denominator of two fractions and rewrite them over it. It is the key step before adding, subtracting, or comparing fractions. Enter two fractions to get the LCD and the converted numerators, with the working shown for learning.
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Open calculator →Frequently Asked Questions
What is the least common denominator?
It is the smallest number that both denominators divide into evenly — the least common multiple of the denominators. For 4 and 6 it is 12, the smallest number both 4 and 6 go into.
How do you find a common denominator?
Find the least common multiple of the denominators. A fast method is to multiply the denominators and divide by their greatest common divisor, which gives the least common denominator directly.
Why do fractions need a common denominator?
Because you can only add, subtract or compare fractions when they are divided into equal-sized pieces. The common denominator makes the pieces the same size so the numerators can be combined.
Is the least common denominator the same as the LCM?
Yes. The least common denominator of two fractions is exactly the least common multiple of their denominators, just used in the context of fractions.
Do I have to use the least common denominator?
No — any common denominator works, such as the product of the denominators. But the least common denominator keeps the numbers smallest and the final fraction easiest to simplify.
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