Hi,

On 11 Feb., 09:56, Simon King <simon.k...@uni-jena.de> wrote:
> Well, I had the impression that a couple of people are in favour of
> the following:
>  gcd(a/b,c/d) := gcd(a,c)/lcm(b,d)
>  lcm(a/b,c/d) := lcm(a,c)/gcd(b,d)

It just occurs to me that I am incredibly stupid.

The definition above wouldn't work at all, it isn't even well-defined.
Just replace gcd(1/4,1/6) by gcd(3/12,9/54). You obtain gcd(1,1)/
lcm(4,6) = 1/12,  but gcd(3,9)/lcm(12,54) = 1/36.

Does anyone have a better idea? Would it be a correct definition if
one insisted on reduced fractions?

Cheers,
Simon

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