## `ilcm` -- the least common multiple of integers

#### Introduction

`ilcm(`i1, i2...`)` computes the least common multiple of the integers i1, i2, ...

#### Call(s)

`ilcm(i1, i2...)`

#### Parameters

`i1, i2...` | - | arithmetical expressions representing integers

#### Returns

a nonnegative integer, or a symbolic `ilcm` call.

#### Related Functions

`content`, `factor`, `gcd`, `gcdex`, `icontent`, `ifactor`, `igcd`, `igcdex`, `lcm`

#### Details

- `ilcm` computes the least common nonnegative multiple of a sequence of integers. `ilcm` with a single numeric argument returns its absolute value. `ilcm` returns `1` when all arguments are `1` or `-1` or no argument is given.
- `ilcm` returns an error message when one of the arguments is a number but not an integer. If at least one of the arguments is `0`, then `ilcm` returns `0`. Otherwise, if one argument is not a number, then a symbolic `ilcm` call is returned.

- `ilcm` is a function of the system kernel.

#### Example 1

We compute the least common multiple of some integers:

    >> ilcm(-10, 6), ilcm(6, 10, 15)

                                      30, 30

    >> a := 4420, 128, 8984, 488:
       ilcm(a), ilcm(a, 64)

                              9689064320, 9689064320

The next example shows some special cases:

    >> ilcm(), ilcm(0), ilcm(1), ilcm(-1), ilcm(2)

                                   1, 0, 1, 1, 2

If one argument is not a number, then the result is a symbolic `ilcm` call, except in some special cases:

    >> delete x:
       ilcm(a, x), ilcm(0, x)

                         ilcm(4420, 128, 8984, 488, x), 0

    >> type(ilcm(a, x))

                                      "ilcm"

#### Changes

- If one of the arguments is `0`, then `ilcm` returns `0`.

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