LCD Calculator — Least Common Denominator
Enter two or three denominators and instantly find their Least Common Denominator — the smallest integer you can use as a shared denominator to add or subtract those fractions.
The smallest integer divisible by all entered denominators
- 1
GCD of denominators
GCD(4, 6) = 2The GCD is found with the Euclidean algorithm. - 2
LCD = a × b ÷ GCD
4 × 6 ÷ 2 = 12
这个计算器是如何工作的？
LCD(a, b) = LCM(a, b) = |a × b| / GCD(a, b). Find the GCD using the Euclidean algorithm, divide it into the product of the two denominators, and that gives the smallest shared denominator. For three denominators apply LCM twice: LCM(LCM(a,b), c).
公式
How this is calculated
The Least Common Denominator of a set of fractions is simply the Least Common Multiple (LCM) of their denominators. To add or subtract fractions, you need them all to share the same denominator, and using the smallest one (the LCD) keeps numbers manageable.
The algorithm works by repeatedly applying the Euclidean method: GCD(a, b) is found by dividing a by b and taking the remainder until the remainder is zero; LCM(a, b) = |a × b| / GCD(a, b). For three denominators the result is LCM(LCM(a, b), c). Once the LCD is known, each original denominator is divided into it to give the multiplier you must apply to that fraction's numerator before combining.
This calculator only accepts positive integers because denominators of standard fractions must be whole numbers. It does not simplify the resulting fractions — that step comes after you add or subtract the equivalent numerators.
常见问题
They are the same operation applied in context. The Least Common Multiple (LCM) is the mathematical concept: the smallest positive integer divisible by all given numbers. The Least Common Denominator (LCD) is the LCM applied specifically to the denominators of fractions, so you can add or subtract those fractions.
Divide the LCD by each denominator to get a multiplier, then multiply both the numerator and denominator of each fraction by its multiplier. For example, 1/4 + 1/6: LCD = 12, multiply 1/4 by 3/3 to get 3/12, multiply 1/6 by 2/2 to get 2/12, then add: 5/12.
Yes — when one denominator is already a multiple of the others. For example, with denominators 3 and 6, LCD = 6 because 6 is a multiple of 3. In that case only the smaller denominator fraction needs to be scaled up.
也称为
TG we-Calculate Editorial Team. (2026). LCD Calculator — Least Common Denominator [Online calculator]. TG we-Calculate. https://we-calculate.com/zh/calculator/lcd-calculator
TG we-Calculate Editorial Team. "LCD Calculator — Least Common Denominator." TG we-Calculate. 2026. https://we-calculate.com/zh/calculator/lcd-calculator.
TG we-Calculate Editorial Team, "LCD Calculator — Least Common Denominator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/zh/calculator/lcd-calculator
@misc{wecalculate_lcd_calculator, title = {LCD Calculator — Least Common Denominator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/zh/calculator/lcd-calculator}}, year = {2026}, note = {TG we-Calculate} }
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