# LCD Calculator – Least Common Denominator

URL: https://speedycalculator.com/calculators/math/lcd/
Last updated: 2026-10-30

> The LCD calculator finds the least common denominator of two to five fractions and rewrites each fraction over it, ready to add, subtract or compare.

## Inputs

- Number of fractions
- Fraction form
- Fraction 1: whole
- Fraction 1: numerator
- Fraction 1: denominator
- Fraction 2: whole
- Fraction 2: numerator
- Fraction 2: denominator
- Fraction 3: whole
- Fraction 3: numerator
- Fraction 3: denominator
- Fraction 4: whole
- Fraction 4: numerator
- Fraction 4: denominator
- Fraction 5: whole
- Fraction 5: numerator
- Fraction 5: denominator

## Results

- Least common denominator
- Equivalent fractions
- Steps

## Formula

```
LCD = LCM(d₁, d₂, …, dₖ)
```

## Explanation

The least common denominator is the smallest number every denominator divides into. Using it to add or compare fractions keeps the numbers as small as possible.

### How to use the LCD Calculator - Least Common Denominator

- **Number of fractions**
- **Fraction form**
- **Fraction 1: whole**
- **Fraction 1: numerator**
- **Fraction 1: denominator**
- **Fraction 2: whole**
- **Fraction 2: numerator**
- **Fraction 2: denominator**
- **Fraction 3: whole**
- **Fraction 3: numerator**
- **Fraction 3: denominator**
- **Fraction 4: whole**
- **Fraction 4: numerator**
- **Fraction 4: denominator**
- **Fraction 5: whole**
- **Fraction 5: numerator**
- **Fraction 5: denominator**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Each fraction is simplified, then the least common multiple of the denominators is found. Every fraction is scaled up to that denominator.

## Worked example

Inputs — Number of fractions: 2; Fraction form: Simple fraction; Fraction 1: numerator: 1; Fraction 1: denominator: 4; Fraction 2: numerator: 5; Fraction 2: denominator: 6.

Results — **Least common denominator = 12**; Equivalent fractions = 1/4 = 3/12
5/6 = 10/12; Steps = Denominators (after simplifying): 4, 6
The LCD is the least common multiple of the denominators: 12.

## Key terms

- **Least common denominator**: The smallest common multiple of the denominators.

## FAQ

**What is the LCD of 1/4 and 5/6?**
12.

**Is the LCD the same as the LCM?**
The LCD is the LCM of the denominators.

**Can I just multiply the denominators?**
That gives a common denominator, but not always the least one.

**Why simplify fractions first?**
A simplified fraction may need a smaller common denominator.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Fraction](https://mathworld.wolfram.com/Fraction.html)