Fractions can only be added, subtracted or compared directly when they share a denominator. The least common denominator (LCD) is the smallest one they can all be rewritten over, which keeps the numbers small and the final answer easy to simplify. Enter a list of fractions and this calculator finds the LCD, shows each fraction converted to it, and as a bonus puts the fractions in order and adds them.
How to use the LCD calculator
- Type the fractions separated by commas or semicolons:
1/4, 5/6, 7/15. Mixed numbers such as1 1/2and decimals such as0.25are accepted (decimals are converted to fractions in lowest terms). - Tick Reduce if you want each fraction simplified before the LCD is found.
- The tape shows the LCD, the equivalent fractions, the fractions from smallest to largest and their sum. The table shows the multiplier used for each one.
How to find the LCD
The LCD is the least common multiple of the denominators:
- Factor every denominator into primes.
- For each prime that appears, take its highest power.
- Multiply those powers together.
Worked example: 1/4, 5/6 and 7/15
Factor the denominators: 4 = 2², 6 = 2 × 3, 15 = 3 × 5
Highest powers: 2², 3, 5 → LCD = 4 × 3 × 5 = 60
Rewrite: 1/4 = 15/60 (×15), 5/6 = 50/60 (×10), 7/15 = 28/60 (×4)
Order: 15/60 < 28/60 < 50/60, so 1/4 < 7/15 < 5/6
Add: (15 + 50 + 28)/60 = 93/60 = 31/20 = 1 11/20
LCD vs. any common denominator
Multiplying all the denominators together always produces a common denominator, but it is frequently far larger than necessary:
| Fractions | Product of denominators | LCD |
|---|---|---|
| 1/4, 5/6 | 24 | 12 |
| 3/8, 5/12 | 96 | 24 |
| 1/4, 5/6, 7/15 | 360 | 60 |
| 2/9, 1/12, 5/18 | 1,944 | 36 |
Working with 60ths instead of 360ths means smaller numerators, fewer chances for arithmetic slips and less simplifying at the end.
Shortcuts for spotting the LCD
- One denominator divides the others: it’s the LCD. For 1/3, 5/6 and 7/12, the LCD is 12.
- Denominators share no factors: the LCD is their product. For 2/3 and 4/5, the LCD is 15.
- Check multiples of the largest denominator: for 3/8 and 5/12, test 12, 24 — and 24 works.
Where you need the LCD
- Adding and subtracting fractions — the adding fractions calculator uses the LCD at every step.
- Comparing and ordering fractions — once the denominators match, compare numerators. See the comparing fractions calculator.
- Solving equations with fractional coefficients — multiplying both sides by the LCD clears every fraction at once.
- Measuring — adding 3/8 in. and 5/16 in. on a tape measure means converting to sixteenths.
If you only need the LCM of plain whole numbers, use the LCM calculator.
Frequently asked questions
What is the least common denominator?
The smallest number that every denominator in a set of fractions divides into. It is the least common multiple of the denominators. For 1/4, 5/6 and 7/15 the LCD is 60.
How do I find the LCD of fractions?
Factor each denominator into primes, take every prime with its highest power, and multiply. For denominators 4 = 2², 6 = 2 × 3 and 15 = 3 × 5, the LCD is 2² × 3 × 5 = 60.
How do I rewrite fractions with the LCD?
Divide the LCD by each denominator, then multiply that fraction's numerator and denominator by the result. For 5/6 with an LCD of 60, 60 ÷ 6 = 10, so 5/6 = 50/60.
Can I just multiply the denominators together?
That always gives a common denominator, but often not the least one. For 1/4 and 5/6 the product is 24, while the LCD is 12. Bigger denominators mean bigger numbers to simplify at the end.
Should I simplify the fractions before finding the LCD?
It usually helps. 2/4 and 1/6 have an LCD of 12 as written, but after reducing 2/4 to 1/2 the LCD is only 6. Tick the reduce option to do this automatically.