Least Common Denominator Calculator — LCD of Fractions
Enter two or three fractions to find their Least Common Denominator — the smallest denominator they all share — then see each fraction rewritten with that denominator and the simplified sum.
Smallest denominator all fractions can share
- 1
GCD of the two denominators
GCD(4, 6) = 2Found via the Euclidean algorithm. - 2
LCD = den₁ × den₂ ÷ GCD
4 × 6 ÷ 2 = 12
How does this calculator work?
LCD = LCM of all denominators, found via GCD: LCD(d₁, d₂) = d₁ × d₂ ÷ GCD(d₁, d₂). Rewrite each fraction as n × (LCD ÷ d) over LCD; add the resulting numerators; simplify by dividing by the GCD of sum and LCD. Enter your fractions — the calculator shows each equivalent form and the sum.
Formula
How this is calculated
The Least Common Denominator of a set of fractions is simply the Least Common Multiple of all their denominators. Once you have the LCD, you rewrite each fraction with it: multiply the numerator and denominator by (LCD ÷ original denominator). This produces equivalent fractions — fractions with the same value but a shared bottom number — which can then be added or subtracted by simply combining their numerators.
For two denominators d₁ and d₂, LCD = LCM(d₁, d₂) = |d₁ × d₂| ÷ GCD(d₁, d₂), where the GCD is found using the fast Euclidean algorithm. For three denominators the result is chained: LCD = LCM(LCM(d₁, d₂), d₃). The order does not affect the answer because LCM is commutative and associative.
After the numerators are added over the LCD, the resulting fraction is simplified by dividing both numerator and denominator by their GCD. The LCD is always a whole positive number; it equals the larger denominator when one denominator is already a multiple of the other.
Frequently asked questions
The LCD of a set of fractions equals the LCM of their denominators. They are computed by the same algorithm. The terms are used interchangeably in this context: LCD specifically refers to the LCM of denominators in a fraction problem.
You can only add fractions that refer to equal-sized pieces. 1/4 and 1/6 use different piece sizes; once you convert both to twelfths (3/12 and 2/12) the pieces are the same size, so adding the numerators makes sense. The LCD gives the smallest such shared piece size.
No — the LCD is always ≤ the product of the denominators. It equals the product only when the denominators are coprime (share no common factor). For example LCD(4, 6) = 12, not 24, because 4 and 6 share a factor of 2.
Also known as
TG we-Calculate Editorial Team. (2026). Least Common Denominator Calculator — LCD of Fractions [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/least-common-denominator-calculator
TG we-Calculate Editorial Team. "Least Common Denominator Calculator — LCD of Fractions." TG we-Calculate. 2026. https://we-calculate.com/calculator/least-common-denominator-calculator.
TG we-Calculate Editorial Team, "Least Common Denominator Calculator — LCD of Fractions," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/least-common-denominator-calculator
@misc{wecalculate_least_common_denominator_calculator, title = {Least Common Denominator Calculator — LCD of Fractions}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/least-common-denominator-calculator}}, year = {2026}, note = {TG we-Calculate} }
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