Least Common Denominator (LCD): How to Find It — Even With Variables (2026)

The least common denominator (LCD) of a set of fractions is just the LCM of their denominators. Find that, rewrite each fraction over it, and adding or comparing fractions becomes easy — even when variables are involved.

This guide covers the LCD for plain numbers and for algebraic fractions with variables, with worked examples you can confirm in the LCM Calculator and tidy up with the Fraction Simplifier.

LCD = LCM of the denominators

The lowest (least) common denominator is the smallest number that every denominator divides into — which is exactly the least common multiple of those denominators. So "find the common denominator" and "find the LCM of the denominators" are the same task.

Worked example with numbers

Add 1/6 + 3/8. The LCD is LCM(6, 8). Since 6 = 2 × 3 and 8 = 2³, the LCM is 2³ × 3 = 24. Rewrite: 1/6 = 4/24 and 3/8 = 9/24, so the sum is 13/24. Compute LCM(6, 8) instantly in the LCM Calculator.

Finding the LCD with variables

For algebraic fractions, factor each denominator first, then take the highest power of every distinct factor — the same rule as the numeric LCM. Treat each variable like a prime.

Worked example with variables

For 1/(6x) and 5/(4x²): factor the denominators as 6x = 2 × 3 × x and 4x² = 2² × x². The LCD takes the highest power of each factor: 2² × 3 × x² = 12x². Then 1/(6x) = 2x/(12x²) and 5/(4x²) = 15/(12x²). A "least common denominator calculator with variables" follows this exact factor-by-factor logic.

Don't forget to simplify

After combining, reduce the result to lowest terms by dividing the numerator and denominator by their GCF. The Fraction Simplifier does this in one step and shows the working.