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Mathematica > Mathematics and Algorithms > Polynomial Algebra > Polynomial Division >

Built-in Mathematica Symbol

PolynomialLCM

PolynomialLCM[poly₁, poly₂, ...]
gives the least common multiple of the polynomials poly_i.

PolynomialLCM[poly₁, poly₂, ..., Modulus->p]
evaluates the LCM modulo the prime p.

PolynomialLCM[poly₁, poly₂, ...] will by default treat algebraic numbers that appear in the poly_i as independent variables.

PolynomialLCM[poly₁, poly₂, ..., Extension->Automatic] extends the coefficient field to include algebraic numbers that appear in the poly_i.

The least common multiple of polynomials:

The LCM of univariate polynomials:

The LCM of multivariate polynomials:

The LCM of more than two polynomials:

The LCM of rational functions:

By default, algebraic numbers are treated as independent variables:

With Extension->Automatic, PolynomialLCM detects algebraically dependent coefficients:

Compute the LCM over the integers modulo 2:

By default, PolynomialLCM treats trigonometric functions as independent variables:

With Trig->True, PolynomialLCM recognizes dependencies between trigonometric functions:

The LCM of polynomials is divisible by the polynomials; use PolynomialMod to prove it:

PolynomialGCD finds the greatest common divisor of polynomials: