I would assume that this characterization of the gcd has been asked and answered before, but I could not find a duplicate with Approach0. Perhaps @BillDubuque knows?
Consider the group: $ G = \lbrace e^{\large\frac{s}{\log x}} : s \in \Bbb R \rbrace $,
with multiplication as the operation and $1$ as the identity element.
Is $G$ related to the Poincaré group?
To find out, I first recast $G$ as $H= \lbrace \frac{s}{x} : s \in \Bbb R \rbrace,$ with addition as...