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# lcm

Least common multiple of polynomials

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```lcm(p, q, …)
lcm(f, g, …)
```

## Description

lcm(p, q, ...) calculates the least common multiple of any number of polynomials. The coefficient ring of the polynomials may either be the integers or the rational numbers, Expr, a residue class ring IntMod(n) with a prime number n, or a domain.

All polynomials must have the same indeterminates and the same coefficient ring.

Polynomial expressions are converted to polynomials. See poly for details. FAIL is returned if an argument cannot be converted to a polynomial.

The return value is of the same type as the input polynomials, i.e., either a polynomial of type DOM_POLY or a polynomial expression.

lcm returns 1 if all arguments are 1 or - 1, or if no argument is given. If at least one of the arguments is 0, then lcm returns 0.

Use ilcm if all arguments are known to be integers, since it is much faster than lcm.

## Examples

### Example 1

The least common multiple of two polynomial expressions can be computed as follows:

`lcm(x^3 - y^3, x^2 - y^2);`

One may also choose polynomials as arguments:

```p := poly(x^2 - y^2, [x, y], IntMod(17)):
q := poly(x^2 - 2*x*y + y^2, [x, y], IntMod(17)):
lcm(p, q)```

`delete f, g, p, q:`

## Parameters

 pq, … polynomials of type DOM_POLY fg, … polynomial expressions

## Return Values

Polynomial, a polynomial expression, or the value FAIL.