  Let $G$ be a compact $p$-adic analytic group with no element of order $p$ and
$H$ be its maximal uniform normal subgroup. Let $K$ be a finite extention of
$\mathbb{Q}_p$. We show that the Grothendieck group of the completion of the
algebra of locally analytic distributions on $G$ is isomorphic to
$\mathbb{Z}^c$ where $c$ is the number of conjugacy classes in $G/H$ relative
prime to $p$, provided that $K$ is big enough. In addition we will see the
algebra $K[[G]]$ of continuous distributions on $G$ has the same Grothendieck
group.
