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Least Common Denominator Calculator
Type two or more fractions to find their least common denominator (LCD). The calculator shows the prime factorisation of each denominator, rewrites every fraction over the LCD, orders them from smallest to largest and adds them up.
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Separate with commas or new lines. Mixed numbers (2 1/3), whole numbers and decimals work too.
Enter your values to see the result.
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How to use the Least Common Denominator Calculator
- Enter your fractions separated by commas, like 1/4, 5/6, 3/8.
- Optionally tick 'Simplify each fraction first'.
- Press Find LCD (results update as you type).
- Read the LCD and the equivalent fractions.
- Follow the steps and the table to see the multiplier for each fraction.
LCD by prime factorisation
| Step | Example: 2/3, 7/12, 5/18 |
|---|---|
| 1. Factor each denominator | 3 = 3; 12 = 2² × 3; 18 = 2 × 3² |
| 2. Highest power of each prime | 2², 3² |
| 3. Multiply them | LCD = 4 × 9 = 36 |
| 4. Rewrite each fraction | 24/36, 21/36, 10/36 |
Shortcut for two denominators: LCD(a, b) = a × b ÷ GCF(a, b). For 12 and 18: 216 ÷ 6 = 36.
Common LCDs
| Denominators | LCD |
|---|---|
| 2, 3 | 6 |
| 2, 3, 4 | 12 |
| 3, 4, 5 | 60 |
| 4, 6, 8 | 24 |
| 6, 8, 12 | 24 |
| 5, 10, 15 | 30 |
| 8, 12, 18 | 72 |
| 2 through 10 | 2,520 |
Frequently asked questions
What is the least common denominator?
The least common denominator (LCD) of a set of fractions is the smallest number that every denominator divides into. It is the least common multiple (LCM) of the denominators. For 1/4, 5/6 and 3/8 the LCD is 24.
How do I find the LCD?
Factor each denominator into primes, then multiply each prime that appears using its highest power. For 4 = 2², 6 = 2 × 3 and 8 = 2³, the LCD is 2³ × 3 = 24.
How do I convert fractions to the LCD?
Divide the LCD by each denominator and multiply the numerator and denominator by that number. With LCD 24: 1/4 = 6/24, 5/6 = 20/24 and 3/8 = 9/24.
Why use the least common denominator instead of any common denominator?
Any common multiple works (multiplying all denominators always gives one), but the LCD keeps the numbers as small as possible, so adding, subtracting and comparing fractions needs less simplifying afterwards.
Should I simplify fractions before finding the LCD?
It can make the LCD smaller. For 2/4 and 1/6 the LCD of the denominators as written is 12, but after simplifying 2/4 to 1/2 the LCD is 6. Both are correct; textbooks usually want the LCD of the fractions as given.
What about mixed numbers?
Convert them to improper fractions first: 2 2/3 = 8/3. The denominator, and so the LCD, stays the same. This calculator does the conversion automatically.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.
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