# [racket-dev] feature request: gcd, lcm for rationals

On Dec 9, 2011, at 3:31 PM, Daniel King wrote:
>* On Fri, Dec 9, 2011 at 15:27, Carl Eastlund <cce at ccs.neu.edu> wrote:
*>>* What does "divides" even mean in Q? I think we need David to explain
*>>* what his extension of GCD and LCM means here, in that "divisors" and
*>>* "multiples" are fairly trivial things in Q.
*>*
*>* I don't suppose to understand all the math on this page, but I think
*>* it uses the same definition that dvh is using.
*>*
*>* http://mathworld.wolfram.com/GreatestCommonDivisor.html
*
Interesting: the Mathematica people have extended the gcd function from the integers to the rationals, not by applying the usual definition of gcd to Q (which would indeed be silly, as everything except 0 divides everything else), but by coming up with a different definition which, when restricted to integers, happens to coincide with the usual definition of gcd.
I would wonder: is this the ONLY "reasonable" function on rationals which, when restricted to integers, coincides with the usual definition of gcd?
Stephen Bloch
sbloch at adelphi.edu