Greatest Common Denominator Calculator — LCD for Fractions
Enter two fractions (numerator and denominator for each) and the calculator finds the greatest common divisor of their denominators, the least common denominator (LCD) needed to add or subtract them, their equivalent forms with that common denominator, and the simplified sum and difference.
The smallest denominator both fractions can share — equals LCM of the two denominators
- 1
GCD of denominators
GCD(3, 4) = 1Found via the Euclidean algorithm: repeatedly divide the larger by the smaller until the remainder is 0. - 2
LCD = D₁ × D₂ ÷ GCD
3 × 4 ÷ 1 = 12
How does this calculator work?
GCD of denominators is found via the Euclidean algorithm; LCD = LCM(d₁, d₂) = d₁ × d₂ / GCD(d₁, d₂). For 1/3 + 1/4: GCD(3,4) = 1, LCD = 12, equivalent fractions are 4/12 and 3/12, sum = 7/12.
Formula
How this is calculated
To add or subtract fractions with different denominators you must convert them to a common denominator — the smallest suitable value is the least common denominator (LCD), which equals the least common multiple (LCM) of the two denominators. The most efficient way to compute LCM(d₁, d₂) uses the identity LCM = d₁ × d₂ / GCD(d₁, d₂), where GCD is found by the Euclidean algorithm (repeatedly replacing the larger number with the remainder of dividing by the smaller, until the remainder is zero).
Once the LCD is known, each fraction is scaled to an equivalent form with that denominator: n₁ becomes n₁ × (LCD/d₁) over LCD, and n₂ becomes n₂ × (LCD/d₂) over LCD. Adding or subtracting the scaled numerators then gives the exact rational result, which is further simplified by dividing numerator and denominator by their GCD.
Note: "greatest common denominator" is an informal term — mathematically there is no "greatest" common denominator (you can always multiply by 2 to get a larger common one). What people usually mean is the GCD of the denominators, which this calculator reports, or the LCD (which is actually the least/smallest common denominator).
Frequently asked questions
The GCD of the denominators is the largest number that divides both of them. The LCD (least common denominator) is the smallest number divisible by both — i.e., their LCM. The two are related: LCD = d₁ × d₂ / GCD(d₁, d₂). For 1/4 and 1/6: GCD(4, 6) = 2, LCD = 24/2 = 12.
Fractions with different denominators measure in different "units" — thirds, quarters and so on. To combine them you must first convert to the same unit. Choosing the LCD minimises the size of the numbers you work with, making simplification easier at the end.
Yes — negative numerators are handled correctly. Enter a negative numerator (e.g. −1) and the sum and difference will carry the correct sign. Only denominators must be positive (a negative denominator is equivalent to negating the numerator, which you can do before entering).
Also known as
TG we-Calculate Editorial Team. (2026). Greatest Common Denominator Calculator — LCD for Fractions [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/greatest-common-denominator-calculator
TG we-Calculate Editorial Team. "Greatest Common Denominator Calculator — LCD for Fractions." TG we-Calculate. 2026. https://we-calculate.com/calculator/greatest-common-denominator-calculator.
TG we-Calculate Editorial Team, "Greatest Common Denominator Calculator — LCD for Fractions," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/greatest-common-denominator-calculator
@misc{wecalculate_greatest_common_denominator_calculator, title = {Greatest Common Denominator Calculator — LCD for Fractions}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/greatest-common-denominator-calculator}}, year = {2026}, note = {TG we-Calculate} }
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