  We consider any cancellative monoid $M$ equipped with a discrete degree map
$deg:M\to R_{\ge0}$ and associated generating function $P(t)=\sum_{m\in
M}t^{deg(m)}$, called the growth function of $M$. We also introduce, using some
towers of minimal common multiple sets in $M$, another signed generating
function $N(t)$, called the skew-growth function of $M$. We show that these
functions satisfy the inversion formula $P(t)N(t)=1$. In case the monoid is the
set of positive integers with ordinary product structure and the degree map is
logarithm function, using the coordinate change $t=exp(-s)$, the inversion
formula turns out to be the Euler product formula for the Riemann's zeta
function.
