gcd, lcm  greatest common divisor and least common multiple
LIBRARY
(import (rnrs)) ;R6RS
(import (rnrs base)) ;R6RS
(import (scheme r5rs)) ;R7RS
(import (scheme base)) ;R7RS
SYNOPSIS
(gcd number ...)
(lcm number ...)
DESCRIPTION
These procedures return the greatest common divisor and the least
common multiple of their arguments, respectively. The result is always
nonnegative. The arguments must be integers.
 Greatest common divisor

If all arguments are zero, or no arguments are given, then
gcd
returns zero. Otherwise the greatest common divisor is the largest
integer that divides each of the arguments.
 Least common multiple

If there are no arguments then 1 is returned.
If one of the arguments is zero then zero is returned.
Otherwise
lcm
returns the smallest positive integer that is divisible by each of the
arguments.
RETURN VALUES
Returns a nonnegative number object.
EXAMPLES
(gcd 32 36) => 4
(gcd) => 0
(lcm 32 36) => 288
(lcm 32.0 36) => 288.0
(lcm) => 1
RATIONALE
The
gcd
procedure is needed internally in Scheme implementations for rational
number support. Its implementation is not trivial, so it makes sense
to provide it to users as well. The
lcm
procedure is a natural complement which is easily implemented once
gcd
is available.
COMPATIBILITY
These procedures are identical in all RnRS revisions since R2RS. An
example with an inexact number was added in R4RS, but the signature
did not change.
R7RS implementations that do not support arbitrarily large exact
integers will not always be able to represent the mathematically
expected result of
lcm.
ERRORS
These procedures can raise exceptions with the following condition types:
 &assertion (R6RS)

An argument was outside its domain.
 R7RS

The assertions described above are errors.
Implementations may signal an error, extend the procedure's
domain of definition to include such arguments,
or fail catastrophically.
SEE ALSO
numerator(3scm)
STANDARDS
R4RS,
IEEE Scheme,
R5RS,
R6RS,
R7RS
HISTORY
The first Scheme report to name these procedures was R2RS.
Nevertheless, Scheme has always had a
gcd
procedure because one was present even in MacLISP (see the
LISP/MACLISP Reference Manual, 1973, Moon et al). The MacLISP version
did not work with inexact numbers.
An algorithm for computing
gcd
appears in Euclid's Elements (circa 300 BCE).
AUTHORS
This page is part of the
schememanpages
project.
It includes materials from the RnRS documents.
More information can be found at
https://github.com/schemedoc/manpages/
.
BUGS
Ikarus Scheme 0.0.4 has the following bug:
(gcd 1) => 1 ; wrong! should be 1
Markup created by unroff 1.0sc, March 04, 2023.