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Result
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Formula Used
For fractions in lowest terms \( \frac{a_i}{b_i} \), the least common multiple of the set is
\(\displaystyle \mathrm{LCM}\left(\frac{a_1}{b_1},\dots,\frac{a_k}{b_k}\right) = \frac{\mathrm{LCM}(a_1,\dots,a_k)}{\gcd(b_1,\dots,b_k)}\).
- Each input fraction is simplified first by dividing by \(\gcd(|a_i|,|b_i|)\).
- Signs are normalized so denominators are positive; the result is non‑negative.
- \(\mathrm{LCM}\) is computed via prime‑factor exponents or pairwise identities.
If any fraction equals zero, the LCM is zero.
How to Use
- Enter two or more fractions using numerators and denominators.
- Keep “Auto‑simplify inputs” enabled for consistent results.
- Click “Compute LCM of Fractions”. Review steps shown below.
- Use “Download CSV” or “Download PDF” to save the results.
- Adjust rows to match your data and recompute quickly.
Example Data
| Set | Fractions | LCM of Fractions |
|---|---|---|
| A | 1/2, 3/4 | 3/2 |
| B | 3/10, 9/20 | 9/10 |
| C | 2/3, 3/5 | 6 |
| D | 4/9, 10/27, 8/3 | 8/1 |
These examples assume prior simplification and positive denominators.
FAQs
It is the smallest non‑negative number that is a multiple of every given fraction.
The closed‑form formula assumes lowest terms. Simplification ensures correct numerator and denominator extraction.
We use pairwise reduction and, for display, prime‑factor exponents choosing maxima for LCM and minima for GCD.
Signs are normalized to numerators, denominators kept positive. The final LCM is non‑negative.
If any fraction equals zero, every common multiple is zero; the LCM is zero.
Division by zero is undefined. Such rows are ignored and flagged as invalid.
No. LCM and GCD are commutative and associative; the result is independent of order.