Least Common Denominator Calculator

Before you can add or subtract fractions with different denominators, both fractions need to be rewritten over the same denominator. The least common denominator (LCD) is the smallest number that works for the job — using it keeps the numbers as small as possible throughout the calculation.

How to Find the Least Common Denominator (step by step)

Step One: Find the greatest common divisor (GCD) of the two denominators

gcd(6, 8) = 2

Step Two: Divide the product of the denominators by the GCD

LCD = (denominator A × denominator B) ÷ GCD
LCD = (6 × 8) ÷ 2 = 24

Step Three: Scale each numerator to match the new denominator

Divide the LCD by each fraction’s original denominator to get its scale factor, then multiply that fraction’s numerator by the same factor.

First fraction:  1/6 → scale factor = 24 ÷ 6 = 4  →  new numerator = 1 × 4 = 4  →  4/24
Second fraction: 5/8 → scale factor = 24 ÷ 8 = 3  →  new numerator = 5 × 3 = 15 →  15/24

With the calculator’s default values, the LCD of 6 and 8 is 24, and the two fractions become 4/24 and 15/24 — both now sharing the same denominator, ready to add or subtract directly.

What your results mean

The least common denominator is the smallest shared denominator both fractions can use. The two new numerator values are what each original fraction’s numerator becomes once its fraction is rewritten over that shared denominator — the fractions’ values haven’t changed, only how they’re expressed.

Once both fractions share the LCD, adding or subtracting them is as simple as combining the numerators, since the denominators already match.

Common denominator pairs

Denominators	GCD	LCD
3, 4	1	12
4, 6	2	12
6, 8	2	24
6, 9	3	18
5, 10	5	10

Notice the LCD isn’t always the two denominators multiplied together — when they share a factor (like 6 and 8, which share a factor of 2, or 6 and 9, sharing a factor of 3), the LCD comes out smaller than that product.

For the full addition or subtraction after finding the LCD, use the adding fractions calculator or subtracting fractions calculator directly — both find the LCD automatically as part of the calculation.

About the formula: The LCD is the least common multiple (LCM) of the two denominators. Multiplying each fraction's numerator by whatever factor scales its denominator up to the LCD keeps the fraction's value unchanged.

Frequently Asked Questions

What's the difference between the LCD and the LCM?+

Nothing mathematically — the LCM (least common multiple) is the general term for the smallest shared multiple of any set of numbers. The LCD (least common denominator) is that same number, specifically when it's being used as a denominator for a set of fractions.

Why not just multiply the two denominators together?+

Multiplying denominators always gives *a* common denominator, but not always the smallest one. For 6 and 8, multiplying gives 48, while the actual LCD is 24 — using 48 means bigger numbers and more simplifying at the end for no benefit.

Do I need the LCD to add or subtract fractions?+

You need *a* common denominator, and the LCD is simply the smallest one, which keeps the arithmetic easier. Any common denominator works and gives the same final answer once fully simplified.