Well, looking at http://mathworld.wolfram.com/LeastCommonMultiple.html they first define LCM in terms of prime factorizations of the arguments, and negative numbers do not have prime factorizations. But then they go on to extend the definition...
I note that most of the references there are quite recent, which suggests invented terminology rather than any sort of stable tradition. There is a book from 1951 listed as a reference for that page, I would be curious to see if it treats this issue of negative numbers. That said: lcm0=: * % +. NB. equivalent to J's definition lcm1=: |@* % +. NB. equivalent to Wikipedia description The wolfram page says that least common multiple is idempotent (-: lcm0 )_1 0 but if we use the other definition: (-: lcm1)_1 0 ... it still does not work. And if we look at the distributive property: (_1 * lcm0/2 3 4) -: lcm0/ _1*2 3 4 1 (_1 * lcm1/2 3 4) -: lcm1/ _1*2 3 4 0 J's definition has this distributive property where the current wikipedia definition does not. I guess I just need to ignore negative arguments, if I want a consistent definition for LCM. -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
