Fraction Calculator guide
How to Find the Least Common Denominator
The least common denominator is the smallest number that all your denominators divide into. For 6 and 8 it is 24. You can find it by listing multiples of the larger denominator until one is divisible by the other, or by using prime factorisation.
What you are looking for
The least common denominator (LCD) is the smallest number that every denominator in your problem divides into evenly.
For 6 and 8, both divide into 24, 48 and 72 — but 24 is the smallest, so that is the LCD.
It is worth saying plainly: any common denominator gives the right answer. The "least" one just keeps the numbers manageable and usually means you do not need to simplify at the end.
Method 1 — just multiply them
Multiplying the denominators together always gives a common denominator. For 6 and 8 that is 48, which works fine.
It is not the smallest, so your numbers will be larger and you will probably need to simplify at the end. But it takes no thought at all.
If the denominators are small, or you are short of time in an exam, this is a perfectly reasonable choice. Getting a correct answer with a bit of extra simplifying beats getting stuck hunting for the LCD.
Method 2 — count up in multiples
Take the larger denominator and count up in its multiples until you hit one the smaller one divides into.
For 6 and 8, count in 8s: 8 (6 does not divide it), 16 (no), 24 (yes, 6 × 4). So the LCD is 24.
Starting from the larger number matters — it gets you there in fewer steps. This method is quick for small denominators and needs nothing memorised.
Method 3 — prime factors
This is the reliable method for awkward numbers, and the one worth learning properly.
Break each denominator into primes. 6 = 2 × 3. 8 = 2 × 2 × 2.
Then take the highest count of each prime across both. The most 2s in any one denominator is three (from the 8). The most 3s is one (from the 6).
So the LCD is 2 × 2 × 2 × 3 = 24.
This scales to any numbers and to more than two fractions, where the counting method starts getting tedious.
Using it
Once you have the LCD, rewrite each fraction over it. For 5/6 + 3/8 with an LCD of 24:
5/6 becomes 20/24, since 6 × 4 = 24 so the top is multiplied by 4 too.
3/8 becomes 9/24, since 8 × 3 = 24 so the top is multiplied by 3.
Adding: 20/24 + 9/24 = 29/24, which is 1 5/24 as a mixed number.
Special cases worth noticing
- If one denominator divides evenly into the other, the larger one is the LCD. For 3 and 12, it is 12 — nothing to work out.
- If the two denominators share no factors, the LCD is their product. For 5 and 7, it is 35.
- If they are equal, there is nothing to do. Add straight away.
