Polynomial LCM Calculator
Exact polynomial LCM over rational coefficients from bounded integer input, normalized monic; zero result is ["0"], rational coefficients are exact decimal numerator/denominator strings.
Description
Polynomial least common multiples are defined up to multiplication by a nonzero constant.
Polynomial least common multiples are defined up to multiplication by a nonzero constant. Monic normalization gives a reproducible result over rational coefficients.1
Exact polynomial LCM over rational coefficients from bounded integer input, normalized monic; zero result is ["0"], rational coefficients are exact decimal numerator/denominator strings.
When to use Polynomial LCM Calculator
Use this tool to exact polynomial LCM over rational coefficients from bounded integer input, normalized monic; zero result is ["0"], rational coefficients are exact decimal numerator/denominator strings.
Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
How to use Polynomial LCM Calculator and understand its results
- Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
- Enter leftPolynomial, rightPolynomial using the field table and calculation rules, then run the tool.
- Read monicLcmCoefficients. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| leftPolynomial | Left polynomial | list of number | Required |
| rightPolynomial | Right polynomial | list of number | Required |
Supply nonempty constant-first signed integer lists of at most 13 entries and coefficient magnitudes ≤one million. Trim high-degree zeros and use exact rational polynomial arithmetic. Return constant-first fraction strings; if either polynomial is zero, return ["0"].
monic LCM = monic[(left/GCD) × right] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| monicLcmCoefficients | Monic lcm coefficients | list of string |
{
"input": {
"leftPolynomial": [
-1,
0,
1
],
"rightPolynomial": [
-2,
1,
1
]
},
"output": {
"monicLcmCoefficients": [
"-2",
"-1",
"2",
"1"
]
}
}Limitations and assumptions
Rational numerator/denominator components are bounded to 4096 digits. Monic output may contain fractions even with integer input.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Polynomial GCD Calculator: Exact polynomial GCD over rational coefficients from bounded integer input, normalized monic; zero result is ["0"], rational coefficients are exact decimal numerator/denominator strings. For a complementary task, use Extended GCD Polynomial Calculator: Compute exact rational polynomial Bézout witnesses u*f+v*g=monic gcd for degree≤12 integer input; coefficient strings preserve fractions and zero/zero returns all zeros.
References
-
Polynomial LCM Calculator — tool.io
Similar or alternative tools
- Polynomial GCD Calculator
Exact polynomial GCD over rational coefficients from bounded integer input, normalized monic; zero result is ["0"], rational coefficients are exact decimal numerator/denominator strings.
- Extended GCD Polynomial Calculator
Compute exact rational polynomial Bézout witnesses u*f+v*g=monic gcd for degree≤12 integer input; coefficient strings preserve fractions and zero/zero returns all zeros.