Least Common Denominator Calculator
The least common denominator of two or more fractions — enter the denominators and get the smallest one they all divide into.
The least common denominator is just the least common multiple of the denominators, under a different name.
How the least common denominator calculator works
The least common denominator is just the least common multiple of the denominators, under a different name. Adding 1/4 and 1/6 needs a denominator both 4 and 6 divide into; the smallest is 12, so the sum becomes 3/12 + 2/12 = 5/12.
Multiplying the denominators always gives a workable common denominator — 24 here — but not the smallest, which leaves more reducing to do at the end. Using the LCD keeps the numbers small throughout.
Formula: gcd(a, b) = gcd(b, a mod b); lcm(a, b) = |a × b| / gcd(a, b)
Worked examples
| Inputs | Least common multiple | Note |
|---|---|---|
| Denominators 4 and 6 | 12 | LCD 12 |
| Thirds, quarters and sixths | 12 | LCD 12 |
| Denominators with nothing in common | 35 | LCD 35 — their product |
FAQFrequently asked questions
What is the least common denominator?
The smallest number every denominator divides into — 12 for quarters and sixths.
How is it different from the LCM?
It is not: the LCD of a set of fractions is the LCM of their denominators.
Why not just multiply the denominators?
That works but is often larger than necessary — 4 and 6 give 24, where 12 will do — leaving more reducing at the end.
How do I use the LCD to add fractions?
Rewrite each fraction over the LCD, then add the numerators: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
What if the denominators share no factors?
Then the LCD is simply their product, as with 5 and 7 giving 35.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.