# gcd: GCD and LCM Integer Functions

### Description

Greatest common divisor and least common multiple

### Usage

 ```1 2``` ```gcd(a, b, extended = FALSE) Lcm(a, b) ```

### Arguments

 `a, b` vectors of integers. `extended` logical; if `TRUE` the extended Euclidean algorithm will be applied.

### Details

Computation based on the extended Euclidean algorithm.

If both `a` and `b` are vectors of the same length, the greatest common divisor/lowest common multiple will be computed elementwise. If one is a vektor, the other a scalar, the scalar will be replicated to the same length.

### Value

A numeric (integer) value or vector of integers. Or a list of three vectors named `c, d, g`, g containing the greatest common divisors, such that

`g = c * a + d * b`.

### Note

The following relation is always true:

`n * m = gcd(n, m) * lcm(n, m)`

`numbers::extGCD`

### Examples

 ```1 2 3 4``` ```gcd(12, 1:24) gcd(46368, 75025) # Fibonacci numbers are relatively prime to each other Lcm(12, 1:24) Lcm(46368, 75025) # = 46368 * 75025 ```

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