# What is the LCD of my fractions?

Finds the least common denominator (LCD) of two or more fractions and rewrites each fraction over it, with the prime factors of each denominator.

- Page: https://www.acalculator.org/math/lcd-calculator
- JSON spec: https://www.acalculator.org/math/lcd-calculator.json
- Version: 25b8459f9089

## Default answer

Example with the default inputs (Fractions 7/12, 5/18): The LCD is 36.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| f | Fractions | Two or more fractions, whole numbers or mixed numbers, separated by commas, semicolons or new lines. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| lcd | Least common denominator | The least common multiple of the denominators. |
| rewritten | Fractions over the LCD | Each fraction with its numerator and denominator multiplied by LCD ÷ its denominator. |
| steps | Steps | The prime factors of each denominator and the LCD built from the highest powers. |

## Method

LCD = LCM of the denominators: factor each denominator into primes and multiply the highest power of each prime. Each fraction a/b becomes (a × LCD ÷ b)/LCD.

## Assumptions

- Denominators are used as typed. A fraction that is not in lowest terms (2/4) keeps its denominator (4); reduce it first if you want the smallest LCD of the values.
- A whole number has denominator 1. A mixed number w a/b is (w × b + a)/b; a minus sign applies to the whole mixed number.
- Fractions are separated by commas, semicolons or new lines; a space separates the whole part of a mixed number.

## Worked examples

1. f = 7/12, 5/18 gives lcd = 36, rewritten = 7/12 = 21/36; 5/18 = 10/36. Source: OpenStax, Prealgebra 2e, §4.5 Add and Subtract Fractions with Different Denominators (the LCD is the LCM of the denominators), https://openstax.org/books/prealgebra-2e/pages/4-5-add-and-subtract-fractions-with-different-denominators (Example: the LCD of 7/12 and 5/18 is 36).
2. f = 8/15, 11/24 gives lcd = 120, rewritten = 8/15 = 64/120; 11/24 = 55/120. Source: OpenStax, Prealgebra 2e, §4.5 Add and Subtract Fractions with Different Denominators (the LCD is the LCM of the denominators), https://openstax.org/books/prealgebra-2e/pages/4-5-add-and-subtract-fractions-with-different-denominators (Example: the LCD of 8/15 and 11/24 is 120).
3. f = 1 1/2; 2/3; -5/8 gives lcd = 24, rewritten = 1 1/2 = 36/24; 2/3 = 16/24; -5/8 = -15/24. Source: OpenStax, Prealgebra 2e, §4.5 Add and Subtract Fractions with Different Denominators (the LCD is the LCM of the denominators), https://openstax.org/books/prealgebra-2e/pages/4-5-add-and-subtract-fractions-with-different-denominators.
4. f = 2/4, 1/6, 3 gives lcd = 12, rewritten = 2/4 = 6/12; 1/6 = 2/12; 3 = 36/12. Source: OpenStax, Prealgebra 2e, §4.5 Add and Subtract Fractions with Different Denominators (the LCD is the LCM of the denominators), https://openstax.org/books/prealgebra-2e/pages/4-5-add-and-subtract-fractions-with-different-denominators.

## FAQ

### What is the least common denominator?

The LCD of two or more fractions is the least common multiple (LCM) of their denominators: the smallest number every denominator divides into. The LCD of 7/12 and 5/18 is 36.

### How do I find the LCD?

Factor each denominator into primes, take the highest power of each prime that appears, and multiply them. 12 = 2² × 3 and 18 = 2 × 3², so the LCD is 2² × 3² = 36.

### How do I rewrite a fraction over the LCD?

Multiply its top and bottom by LCD ÷ its denominator. For 7/12 with LCD 36, multiply by 3 to get 21/36; for 5/18, multiply by 2 to get 10/36.

### Is the LCD the same as the LCM?

The LCD is the LCM of the denominators. The LCM calculator takes any list of numbers; this page takes fractions and also rewrites them.

### Should I reduce the fractions first?

This page uses the denominators exactly as you type them. 2/4 and 1/6 have LCD 12; reduced to 1/2 and 1/6, the LCD is 6. Reduce first if you want the smallest common denominator of the values.

### Can I use mixed numbers, whole numbers or negatives?

Yes. Type a mixed number as 1 1/2 (a space before the fraction), a whole number as 3 (denominator 1), and a negative as -5/8.

## Sources

- OpenStax, Prealgebra 2e, §4.5 Add and Subtract Fractions with Different Denominators (the LCD is the LCM of the denominators; LCD of 7/12 and 5/18 is 36; of 8/15 and 11/24 is 120). https://openstax.org/books/prealgebra-2e/pages/4-5-add-and-subtract-fractions-with-different-denominators (retrieved 2026-10-02)