Why do I need a common denominator?

Fractions can only be added or subtracted directly once they share the same denominator — the LCD is the smallest such denominator, keeping the numbers as simple as possible.

Is the LCD always the product of the denominators?

No — only when the denominators share no common factors. When they do share factors, the true LCD is smaller than the simple product.

LCD Calculator

Find the least common denominator (LCD) of two or more fractions — the smallest denominator they can all share.

Denominators (comma or space separated — e.g. for 1/4 and 1/6, enter "4, 6")

Least Common Denominator

How It Works

LCD is the LCM of the denominators

The least common denominator of a set of fractions is simply the least common multiple (LCM) of their denominators — the fraction's numerators don't affect it at all.

Example Calculation

For 1/4 and 1/6, the LCD is 12 — both 1/4 (as 3/12) and 1/6 (as 2/12) can be expressed with a denominator of 12.

Common Mistakes

Multiplying the denominators together directly instead of finding their actual least common multiple, which can produce a needlessly large common denominator.
Forgetting to also scale up the numerator when converting a fraction to the common denominator.

Frequently Asked Questions

Why do I need a common denominator?: Fractions can only be added or subtracted directly once they share the same denominator — the LCD is the smallest such denominator, keeping the numbers as simple as possible.
Is the LCD always the product of the denominators?: No — only when the denominators share no common factors. When they do share factors, the true LCD is smaller than the simple product.