# PolynomialLCM

PolynomialLCM[poly1,poly2,]

gives the least common multiple of the polynomials polyi.

PolynomialLCM[poly1,poly2,,Modulusp]

evaluates the LCM modulo the prime p.

# Details and Options • PolynomialLCM[poly1,poly2,] will by default treat algebraic numbers that appear in the polyi as independent variables.
• PolynomialLCM[poly1,poly2,,Extension->Automatic] extends the coefficient field to include algebraic numbers that appear in the polyi.

# Examples

open allclose all

## Basic Examples(1)

The least common multiple of polynomials:

## Scope(3)

The LCM of univariate polynomials:

The LCM of multivariate polynomials:

The LCM of more than two polynomials:

## Generalizations & Extensions(1)

The LCM of rational functions:

## Options(3)

### Extension(1)

By default, algebraic numbers are treated as independent variables:

With , PolynomialLCM detects algebraically dependent coefficients:

### Modulus(1)

Compute the LCM over the integers modulo 2:

### Trig(1)

By default, PolynomialLCM treats trigonometric functions as independent variables:

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

## Properties & Relations(1)

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

PolynomialGCD finds the greatest common divisor of polynomials:

Introduced in 1991
(2.0)
|
Updated in 1996
(3.0)