Math
Least Common Denominator Calculator
Type two to six fractions and get their least common denominator from the prime factorization of every denominator.
The calculator also rewrites each fraction over the LCD with the multiplier used, which is exactly the setup you need before adding, subtracting, or ordering fractions.
One per line or separated by commas. 2 to 6 fractions; mixed numbers and decimals are converted first.
Try an example
Result
Least common denominator
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- LCD as prime factors
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- Fractions over the LCD
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- Multipliers
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- Product of denominators
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the least common denominator is
The The smallest bottom number two fractions can share so you can add or compare them. of a set of fractions is the least common multiple of their The bottom number of a fraction; it says how many equal parts make one whole.: the smallest number every denominator divides into evenly. It is the smallest denominator you can rewrite all the fractions over, which keeps the numbers small when adding, subtracting, or comparing.
Finding the LCD with prime factors
Factor every denominator into A whole number above 1 whose only factors are 1 and itself., then take each prime at the highest power that appears anywhere. For 4, 6, and 9: 4 = 2^2, 6 = 2 × 3, 9 = 3^2. The highest powers are 2^2 and 3^2, so the LCD is 4 × 9 = 36. Multiplying all three denominators would give 216, six times bigger.
| Denominators | Prime factors | LCD | Product |
|---|---|---|---|
| 4, 6 | 2^2; 2 × 3 | 12 | 24 |
| 4, 6, 9 | 2^2; 2 × 3; 3^2 | 36 | 216 |
| 3, 5, 7 | 3; 5; 7 | 105 | 105 |
| 8, 12, 20 | 2^3; 2^2 × 3; 2^2 × 5 | 120 | 1920 |
Rewriting fractions over the LCD
Divide the LCD by each denominator to get that fraction's multiplier, then multiply its The top number of a fraction; it counts how many parts you have. by the same number. 1/4 over 36 uses multiplier 9: 9/36. 5/6 uses 6: 30/36. 7/9 uses 4: 28/36. Now the fractions can be added (67/36) or ordered by numerator.
How to use it
- Type each fraction on its own line or separated by commas.
- Read the LCD and its prime-factor form.
- Use the rewritten fractions and multipliers to continue with adding, subtracting, or comparing.
- Open Show the work to see each denominator's factorization and which one contributed each highest prime power.
How to read the answer
The LCD is the smallest shared denominator. Any common multiple works for arithmetic, but the LCD produces the smallest numerators and the least simplifying afterwards. The multiplier for each fraction is LCD ÷ its denominator.
Common mistakes and edge cases
- The LCD comes from the denominators only; numerators do not affect it.
- Multiplying all denominators gives a common denominator but usually not the least one.
- Use the highest power of each prime, not the sum of the The small raised number saying how many times to multiply the base by itself.: for 4 and 8, the LCD is 8, not 32.
- Convert A whole number written next to a fraction, like 2 1/3. and decimals to fractions first; the calculator does this automatically.
- A denominator of 0 is undefined and is rejected.
Worked examples
Three fractions
1/4, 5/6, 7/9
Least common denominator
36
Two fractions
1/4 and 1/6
Least common denominator
12
Coprime denominators
1/3, 2/5, 4/7
Least common denominator
105
One denominator divides the others
3/8, 1/4, 1/2
Least common denominator
8
Mixed numbers and decimals
1 1/2, 0.75, 2/3
Least common denominator
12
Six fractions
1/2 through 1/7
Least common denominator
420
Only one fraction
Needs at least two
Least common denominator
Error
Zero denominator
1/4 and 1/0
Least common denominator
Error
Frequently asked questions
What is the least common denominator?+
The smallest number that all the denominators divide into evenly. It equals the least common multiple of the denominators.
Is the LCD the same as the LCM?+
Yes. LCD is the name used when the numbers are denominators of fractions; LCM is the general name for the same calculation.
How do you find the LCD of three fractions?+
Factor each denominator into primes and multiply the highest power of every prime that appears. For 4, 6, and 9 that is 2^2 × 3^2 = 36.
Can I just multiply the denominators?+
That always gives a common denominator, but it is only the least one when the denominators share no factors. For 4 and 6, the product is 24 but the LCD is 12.
Why do I need the LCD?+
Fractions can only be added, subtracted, or compared directly when they have the same denominator. The LCD does that with the smallest possible numbers.
Does the LCD calculator work with mixed numbers?+
Yes. Mixed numbers and decimals are converted to fractions first, and their denominators are used.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026