/* 

  Least common multipl (Rosetta code) in Picat.

  http://rosettacode.org/wiki/Least_common_multiple
  """
  Compute the least common multiple of two integers.

  Given m and n, the least common multiple is the smallest positive integer 
  that has both m and n as factors. For example, the least common multiple 
  of 12 and 18 is 36, because 12 is a factor (12 × 3 = 36), and 18 is a 
  factor (18 × 2 = 36), and there is no positive integer less than 36 that 
  has both factors. As a special case, if either m or n is zero, then the 
  least common multiple is zero.

  One way to calculate the least common multiple is to iterate all the multiples 
  of m, until you find one that is also a multiple of n.

  If you already have gcd for greatest common divisor, then this formula 
  calculates lcm.

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

  One can also find lcm by merging the prime decompositions of both m and n. 
  """

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


% import util.
% import cp.


main => go.


go =>
  L = [
        [12,18],
        [-6,14],
        [35,0],
        [7,10],
        [2562047788015215500854906332309589561,6795454494268282920431565661684282819]
      ],
  foreach([X,Y] in L)
     println((X,Y)=lcm(X,Y))
  end,
  
  println('1..20'=lcm(1..20)),
  println('1..50'=lcm(1..50)),

  % println([lcm(I,J): I in 1..10, J in 1..10]),

  nl.

% lcm/2
lcm(X,Y)= abs(X*Y)//gcd(X,Y).

% lcm/3
lcm(X,Y,LCM) => LCM = abs(X*Y)//gcd(X,Y).

lcm(List) = fold(lcm,1,List).

% gcd(List) = fold(gcd,List.first(),List.tail()).