LCD Calculator (Least Common Denominator)

The least common denominator (LCD) is the smallest number that every denominator in a list divides into evenly. You need it to add, subtract or compare fractions that have different denominators. Enter fractions — or just their denominators — to get the LCD, each fraction rewritten over it, the fractions in order and their sum.

How to use this tool

1. Type the fractions separated by commas, for example 1/4, 5/6, 3/8. Mixed numbers like 1 1/2 and whole numbers also work.
2. Or choose “Denominators only” and enter just the bottom numbers.
3. Tick the reduce option if 2/4 should be treated as 1/2.
4. Read the LCD and the equivalent fractions; the table shows what each fraction was multiplied by.

Formula

LCD(a/b, c/d, …) = LCM(b, d, …)

Factor each denominator into primes and take every prime at its highest power. Each fraction is then rewritten by multiplying its top and bottom by LCD ÷ its denominator. For two denominators there is a shortcut: LCM(b, d) = b × d ÷ GCD(b, d).

Example

For 1/4, 5/6 and 3/8: 4 = 2², 6 = 2 × 3 and 8 = 2³, so the LCD is 2³ × 3 = 24. Multiply 1/4 by 6/6, 5/6 by 4/4 and 3/8 by 3/3 to get 6/24, 20/24 and 9/24. Now they are easy to compare — 1/4 < 3/8 < 5/6 — and to add: 6 + 20 + 9 = 35, so the sum is 35/24.