How this calculator works
The least common denominator is the least common multiple of the denominators as entered, before reducing the fractions. Convert mixed numbers to improper fractions, keep denominator magnitudes positive, and compute the common multiple using gcds. Multiply each numerator and denominator by the corresponding factor. Reducing your inputs first can give a smaller common denominator for the same values.
Formula
LCD(d1,...,dn) = lcm(|d1|,...,|dn|), with lcm(a,b) = |ab|/gcd(a,b).
Worked example
The LCD of 1/6 and 1/8 is 24, giving 4/24 and 3/24. For 2/4, 3/6 and 5/9, the entered denominators have least common multiple 36.
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Frequently asked questions
Why not multiply all denominators?
Their product is a common denominator, but shared factors can make it larger than necessary.
Does the calculator reduce inputs first?
No. It preserves the entered denominators so the reported LCD matches those denominators. Simplify first if that is your intended method.
Can I enter a negative denominator?
Yes. Its magnitude is used in the LCD and the sign is transferred to its numerator in the equivalent fraction.