Lowest Common Denominator Calculator — LCD of Fractions
Enter 2–4 denominators to find their lowest common denominator (LCD) — the smallest number you can use as a shared denominator when adding or subtracting fractions. The calculator shows exactly which multiplier to apply to each fraction.
Smallest integer divisible by all entered denominators
GCD(4, 6) via Euclidean algorithm
LCD = (a × b) ÷ GCD(a, b)
Lowest Common Denominator
- 1
GCD(4, 6)
Euclidean algorithm = 2Greatest common divisor via repeated division. - 2
LCM(4, 6) = 4 × 6 ÷ 2
4 × 6 ÷ 2 = 12
How does this calculator work?
LCD = LCM of all denominators = (a × b) / GCD(a, b), extended left to right for more denominators. Enter your denominators to get the LCD instantly, the multiplier to convert each fraction, and a step-by-step Euclidean GCD derivation. Works for 2 to 4 integer denominators.
Formula
How this is calculated
The lowest common denominator of a set of fractions is the smallest positive integer that is divisible by every denominator in the set. Mathematically, this is the least common multiple (LCM) of all the denominators. To convert any fraction x/d to LCD, multiply both numerator and denominator by (LCD / d) — this multiplier is shown for each denominator in the output.
The LCM of two numbers a and b is computed as (a × b) / GCD(a, b), where GCD is the greatest common divisor found via the Euclidean algorithm: repeatedly replace (a, b) with (b, a mod b) until b is zero, at which point a is the GCD. For three or more denominators the LCM is extended one denominator at a time: LCM(a, b, c) = LCM(LCM(a, b), c).
This calculator handles integer denominators only — decimal denominators should first be converted to fractions. The result can grow large when denominators share no common factors (e.g. LCD of 7, 11, 13 = 1001), so inputs are capped at 99,999 each to keep results manageable. If your denominators are very large, consider simplifying each fraction to lowest terms first.
Frequently asked questions
They are the same operation applied in different contexts. LCM (least common multiple) is the general term for the smallest number divisible by both a and b. LCD (lowest common denominator) is the LCM of the denominators of two or more fractions, used specifically to convert fractions to a common base before adding or subtracting them.
Fraction denominators define the "unit" of each piece. You cannot directly add thirds and quarters any more than you can add metres and feet without converting. Converting both fractions to the LCD turns them into the same unit, so the numerators can be added directly: 1/4 + 1/6 → 3/12 + 2/12 = 5/12.
If the denominators are coprime (GCD = 1), the LCD equals their product. For example, LCD(7, 11) = 77. This is mathematically correct but produces large numbers that can be awkward to work with — in that case, just convert both fractions and simplify the result by dividing by GCD of the resulting numerator and denominator.
Also known as
TG we-Calculate Editorial Team. (2026). Lowest Common Denominator Calculator — LCD of Fractions [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/lowest-common-denominator-calculator
TG we-Calculate Editorial Team. "Lowest Common Denominator Calculator — LCD of Fractions." TG we-Calculate. 2026. https://we-calculate.com/calculator/lowest-common-denominator-calculator.
TG we-Calculate Editorial Team, "Lowest Common Denominator Calculator — LCD of Fractions," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/lowest-common-denominator-calculator
@misc{wecalculate_lowest_common_denominator_calculator, title = {Lowest Common Denominator Calculator — LCD of Fractions}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/lowest-common-denominator-calculator}}, year = {2026}, note = {TG we-Calculate} }
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