LCD Calculator - Least Common Denominator
With this LCD calculator you can find the lowest common denominator of up to five fractions.
Lowest common denominator24
Denominators4, 6, 8
GCD of the denominators2
Product of them all192always a common denominator, but rarely the lowest
Building the LCD
| Denominator | Prime factors | Multiply by | Converted |
|---|---|---|---|
| 4 | 2^2 | ×6 | ×6 |
| 6 | 2 × 3 | ×4 | ×4 |
| 8 | 2^3 | ×3 | ×3 |
The method
LCD = lowest common multiple of the denominators
The rules in one place
- Adding and subtracting needs a common denominator first. The lowest common denominator keeps the numbers smallest, but any common denominator works.
- Multiplying needs no common denominator at all — multiply across the top and across the bottom.
- Dividing means multiplying by the reciprocal: flip the second fraction and multiply.
- Reducing divides top and bottom by their greatest common divisor. It never changes the value.
Why lowest terms matter
6/8 and 3/4 are the same number, but 3/4 is easier to compare, easier to check and conventional in an answer. Reducing also keeps later arithmetic small: multiplying unreduced fractions makes the numbers grow fast, and cancelling first avoids that.