Type any set of fractions and this tool locks onto the lowest common denominator the moment you stop typing. It rewrites every fraction over that shared denominator and, when you want the full picture, opens up the prime-factor math sitting behind the answer.
Add up to 5 fractions to find their lowest common denominator instantly. Switch to Mixed Numbers to include whole-number parts.
Enter fractions above to see how their lowest common denominator is built from shared prime factors.
When two or more fractions have different denominators, the lowest common denominator is the smallest whole number that every one of those denominators divides into with nothing left over. Rewriting each fraction over that single shared denominator is what makes adding, subtracting, and comparing fractions possible in the first place.
The lowest common denominator is never smaller than the largest denominator in the group, because it has to be a multiple of every denominator at once. For 1/6 and 1/9, the number has to show up somewhere in both the 6-times table and the 9-times table. The first place that happens is 18, so 18 is the lowest common denominator for that pair.
Because 18 is divisible by both 6 and 9, every fraction in the set can be rewritten with 18 on the bottom without changing its value. You're only ever multiplying by a disguised form of 1, such as 3/3 or 2/2, so 1/6 becomes 3/18 and 1/9 becomes 2/18, the same amount with a new denominator.
Some classrooms and textbooks call this value the "lowest common denominator," others call it the "least common denominator." Both phrases point at the identical number. There's no mathematical distinction between the two, only a difference in the wording a particular course happens to use.
There isn't one single way to land on the lowest common denominator. The right approach usually depends on how large the denominators are and whether you're working with plain fractions or mixed numbers. The three methods below all produce the same answer; they just get there differently.
| Method | Best for | Typical steps |
|---|---|---|
| Listing multiples | Small denominators you can count through by hand | Write out each denominator's multiples until one number appears in every list |
| Prime factorization | Larger denominators or more than two fractions | Factor each denominator into primes, then multiply the highest power of every prime |
| GCF formula | Exactly two denominators, when you already know their GCF | Multiply the two denominators and divide by their greatest common factor |
This is the most direct method for small denominators: write out the multiples of each one, in order, and stop as soon as a number turns up in every list. That first shared value is the lowest common denominator, because nothing smaller could possibly appear in all the lists at once.
Listing multiples gets slow once denominators grow past a dozen or so. Prime factorization scales much better: break every denominator down into the primes that multiply together to build it, then for each prime that shows up anywhere, keep only its highest power across the whole set. Multiply those together and you have the lowest common denominator, guaranteed.
When you're only working with two fractions and you already know (or can quickly find) their greatest common factor, this shortcut skips the factoring step entirely. Multiply the two denominators, then divide by whatever they have in common. What's left is the lowest common denominator.
Mixed numbers add one extra step before any of the methods above can run: the whole-number part has to be folded into the fraction. Multiply the whole number by the denominator, add the numerator, and keep the same denominator. That turns 2 1/3 into 7/3 without changing its value. Once every term is a plain fraction, find the lowest common denominator of the denominators as usual.
Six fully solved problems, moving from a simple two-fraction pair through three-fraction sums and a mixed-number addition, so you can see each method applied to real numbers.