How to Find the Lowest Common Denominator

Which is bigger, 5/6 or 7/8? Most people can’t answer that immediately, and the reason is that fractions with different denominators aren’t directly comparable — the numerators are counting different-sized pieces.

Putting them over a common denominator fixes that, and doing it with the lowest common denominator keeps the arithmetic manageable.

Why the lowest one matters

Any common denominator works. Multiply all the denominators together and you’re guaranteed one: for 4, 6 and 10 that gives 240, and the arithmetic is valid.

It’s also unnecessarily large. The lowest common denominator for those three is 60 — four times smaller — which means smaller numerators, easier addition, and usually no simplifying at the end.

Finding it is a prime factorisation problem. Break each denominator into prime factors, then take each distinct prime at the highest power it appears anywhere:

• 4 = 2²
• 6 = 2 × 3
• 10 = 2 × 5

The primes involved are 2, 3 and 5. The highest power of 2 is 2², of 3 is 3¹, of 5 is 5¹. So the LCD is 2² × 3 × 5 = 60.

That method scales to any number of fractions, which is why it’s worth learning rather than hunting for a common multiple by trial.

Why people get stuck here

• Multiplying everything. It works and produces numbers big enough to make the rest of the problem harder.
• Guessing the multiple. Trial and error works for two small denominators and falls apart with three.
• Forgetting to scale the numerator. Changing the denominator without multiplying the numerator by the same factor changes the value of the fraction.
• Comparing numerators directly. 7/8 and 5/6 cannot be compared by looking at 7 and 5.

How to use it

For adding and subtracting

Fractions can only be added over a shared denominator. Convert both, add the numerators, and simplify if needed. With the LCD, simplification is often unnecessary.

For comparing

Once every fraction is over the same denominator, the numerators are directly comparable. 5/6 becomes 20/24 and 7/8 becomes 21/24, so 7/8 is larger — by one twenty-fourth.

For ordering a set

The same conversion puts a whole list in order at a glance, which is far more reliable than converting each to a decimal and comparing rounded values.

Common mistakes to avoid

• Changing the denominator and leaving the numerator alone.
• Using the product of the denominators and then struggling to simplify a large result.
• Assuming a bigger numerator means a bigger fraction across different denominators.
• Cancelling across an addition — you can simplify a single fraction, not terms across a sum.
• Converting to decimals and comparing rounded values, which fails on close fractions.

How to do it with Lowest Common Denominator Calculator

The Lowest Common Denominator Calculator shows the factorisation as well as the answer.

1. Enter the fractions separated by commas.
2. Read the LCD and the prime factorisation that produced it.
3. Check the converted equivalents — every numerator scaled by the same factor as its denominator.
4. Add or compare using the converted forms.

Other maths tools are in the tools directory.

Frequently asked questions

Why not just multiply the denominators?

It works and gives a valid common denominator, usually a much larger one. Using the LCD keeps the numbers small and often means the answer needs no simplifying at all.

What’s the difference between LCD and LCM?

They’re the same calculation. LCM is the general term for any set of numbers; LCD is what we call it when those numbers are denominators.

Does this help with comparing fractions?

Yes, and it’s the reliable method. Once every fraction is over the same denominator, the numerators can be compared directly.

Final thought

Learn the prime factorisation method rather than hunting for a common multiple. It’s the same effort for two fractions and the only approach that still works for five.

Try the free Lowest Common Denominator Calculator