How to solve it
- Write down the denominators.
- Find their least common multiple (LCM): the smallest number all of them divide exactly.
- That LCM is the least common denominator.
- Convert each fraction: multiply numerator and denominator by LCM ÷ denominator.
4 × 9 = 6 × 6 = 9 × 4 = 36
3/4 = 27/36
1/6 = 6/36
5/9 = 20/36
Result: 36
Common mistake:Wrong: 4, 6 → 2.Right: 4, 6 → 12.The common denominator is a multiple of the denominators, not a divisor. The LCM of 4 and 6 is 12; 2 is their common divisor.
Enter the fractions in the calculator, one per line, and select Calculate. The first line of the result gives the denominator, and below it each fraction appears already rewritten, ready to add, subtract, or compare. The least common denominator of several fractions is the least common multiple (LCM) of their denominators. For the LCM of standalone numbers, use the LCM calculator.
Worked example: 5/6 and 7/15
You want to add 5/6 and 7/15. Which common denominator do you use, and what is the sum?
- Factor the denominators. 6 = 2 × 3 and 15 = 3 × 5.
- Take each prime with its highest power. The LCM of 6 and 15 is 2 × 3 × 5 = 30.
- Find each fraction’s factor. 30 ÷ 6 = 5 and 30 ÷ 15 = 2, so 5/6 = 25/30 and 7/15 = 14/30.
- Add and simplify. 25/30 + 14/30 = 39/30, and dividing by 3 gives 13/10.
Result: denominator 30 and sum 13/10, that is, 1 3/10.
Check: 13/10 − 7/15 = 39/30 − 14/30 = 25/30 = 5/6, so the sum takes you back to the starting fraction.
How the common denominator is found
There are two ways. The first is to list the multiples of the largest denominator until you reach one divisible by the others: for 6 and 15, the multiples of 15 are 15 and 30, and 30 is already divisible by 6. The second is the prime factorization used in the example, which is faster as the numbers grow. Both reach the same number.
To see the LCM with the list of multiples and the factorization step by step, the LCM calculator works with standalone numbers instead of fractions.
Four cases by denominator
Before calculating, it helps to look at the denominators, because sometimes the result is visible at a glance. The table gathers four representative cases and shows how each pair or group looks once rewritten.
| Case | Fractions | Denominator | Rewritten |
|---|---|---|---|
| One divides the other | 1/3 and 5/12 | 12 | 4/12 and 5/12 |
| No common factors | 3/4 and 2/5 | 20 | 15/20 and 8/20 |
| Common factors and three fractions | 1/4, 5/6, and 7/10 | 60 | 15/60, 50/60, and 42/60 |
| Unreduced fraction | 2/4 and 1/3 | 6 | 3/6 and 2/6 |
If one denominator is a multiple of all the others, it is the least common denominator; if they share no factor, the least common denominator is their product. In the other cases, like the third, you need to look at the primes.
Why you use the LCM and not the GCF
The greatest common factor (GCF, also called the GCD) and the LCM are easy to mix up because they come from the same numbers. The GCF is the largest number that divides all of them, and it is used to simplify a fraction. The LCM is the smallest number that all of them divide, and that is what a common denominator needs: each denominator must fit a whole number of times.
The GCF vs. LCM guide compares the two with more examples, and the GCF calculator is the one to use for simplifying.
What to do with the rewritten fractions
Fractions with the same denominator are called like fractions, and those with different denominators are unlike fractions. This calculator turns the second kind into the first. With them, adding fractions and subtracting fractions comes down to working with the numerators, and ordering fractions to sorting the numerators from least to greatest.
To compare just two fractions there is another route, cross multiplication, explained on the compare fractions page. And to see that each rewritten fraction is worth the same as the original, the equivalent fractions page shows why multiplying the numerator and denominator by the same number does not change the value. That operation is called building up to an equivalent fraction; the opposite, dividing by a common factor, is simplifying.
Limits and source
The rewritten fractions are not reduced, because they must share a denominator. A denominator of 0 is not accepted, and each number can have up to 100 digits.
In English, OpenStax’s Prealgebra 2e section Add and Subtract Fractions with Different Denominators defines the LCD of two fractions as the LCM of their denominators and shows how to rewrite fractions over it (accessed October 17, 2026).
Frequently asked questions
How do I find it with three or more fractions?
Work two at a time: find the LCM of the first two denominators, then the LCM of that result with the next one. With 1/3, 1/5, and 1/8, the LCM of 3 and 5 is 15, and the LCM of 15 and 8 is 120. The calculator does the same with up to 20 fractions and rewrites all of them over that denominator.
Do I have to use the least one?
No. Any common multiple of the denominators works and leads to the same result; the least one just keeps the numbers small. For 1/9 + 1/6, using 54 gives 6/54 + 9/54 = 15/54, which you then have to simplify. With 18, the least one, you get 2/18 + 3/18 = 5/18 without that step.
What is the difference from the LCM?
In the calculation, none: the least common denominator is the LCM of the denominators. The use is what changes. The LCM is asked for with standalone numbers, and the least common denominator for fractions that also need to be rewritten. With 2/9 and 7/12, the LCM of 9 and 12 is 36, and the fractions become 8/36 and 21/36.