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########################################################################
##
## Copyright (C) 1994-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave is free software: you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{l} =} lcm (@var{x}, @var{y})
## @deftypefnx {} {@var{l} =} lcm (@var{x}, @var{y}, @dots{})
## Compute the least common multiple of @var{x} and @var{y}, or of the list of
## all arguments.
##
## All inputs must be of the same size, or scalar. All elements must be
## real integer or Gaussian (complex) integer. For complex inputs, the result
## is unique only up to a phase factor (multiplication by +1, +i, -1, or -i),
## and one of the four is returned arbitrarily.
##
## Example code:
##
## @example
## @group
## lcm (5:8, 9:12)
## @result{} 45 30 77 24
## @end group
## @end example
##
## Programming tip: To find the LCM of all the elements of a single array, use
## @code{num2cell} instead of nested calls or a loop:
##
## @example
## @group
## x = 1:10; # vector or array of inputs
## lcm (num2cell (x) @{:@})
## @result{} 2520
## @end group
## @end example
## @seealso{factor, gcd, isprime}
## @end deftypefn
function l = lcm (varargin)
if (nargin < 2)
print_usage ();
endif
if (common_size (varargin{:}) != 0)
error ("lcm: all args must be the same size or scalar");
elseif (! all (cellfun ("isnumeric", varargin)))
error ("lcm: all arguments must be numeric");
endif
l = varargin{1};
for i = 2:nargin
x = varargin{i};
msk = (l == 0 & x == 0);
l .*= x ./ gcd (l, x);
l(msk) = 0;
endfor
if (isfloat (l) && l > flintmax (l))
warning ("Octave:lcm:large-output-float", ...
"lcm: possible loss of precision");
elseif (isinteger (l) && l == intmax (l))
warning ("Octave:lcm:large-output-integer", ...
"lcm: result may have saturated at intmax");
endif
endfunction
%!assert (lcm (3, 5, 7, 15), 105)
## Test input validation
%!error <Invalid call> lcm ()
%!error <Invalid call> lcm (1)
%!error <same size or scalar> lcm ([1 2], [1 2 3])
%!error <arguments must be numeric> lcm ([1 2], {1 2})
%!warning <loss of precision> lcm (num2cell (double (1:47)){:});
%!warning <loss of precision> lcm (num2cell (single (1:47)){:});
%!warning <result .* saturated> lcm (num2cell (uint64 (1:47)){:});
%!warning <result .* saturated> lcm (num2cell (uint32 (1:47)){:});
%!warning <result .* saturated> lcm (num2cell (uint16 (1:47)){:});
%!warning <result .* saturated> lcm (num2cell ( uint8 (1:47)){:});
%!warning <result .* saturated> lcm (num2cell ( int64 (1:47)){:});
%!warning <result .* saturated> lcm (num2cell ( int32 (1:47)){:});
%!warning <result .* saturated> lcm (num2cell ( int16 (1:47)){:});
%!warning <result .* saturated> lcm (num2cell ( int8 (1:47)){:});
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