  Let $K = \mathbb{Q} (\alpha) $ be a pure number field generated by a complex
root $\alpha$ of a monic irreducible polynomial $ F(x) = x^{2^u\cdot 3^v}-m$,
with $m \neq \pm 1$ a square free rational integer, $u$, and $v$ two positive
integers. In this paper, we study the monogenity of $K$. The case $u=0$ or
$v=0$ has been previously studied. We prove that if $m\not\equiv 1$ (mod4) and
$m\not\equiv \pm 1$ (mod9), then $K$ is monogenic. But if $m\equiv 1$ (mod4) or
$m\equiv 1$ (mod9), then $K$ is not monogenic. Some illustrating examples are
given too.
