  Let $c$ be a proper $k$-coloring of a connected graph $G$ and
$\Pi=(C_1,C_2,...,C_k)$ be an ordered partition of $V(G)$ into the resulting
color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to
$\Pi$ is defined to be the ordered $k$-tuple
$c_{{}_\Pi}(v):=(d(v,C_1),d(v,C_2),...,d(v,C_k)),$ where $d(v,C_i)=\min\{d(v,x)
| x\in C_i\}, 1\leq i\leq k$. If distinct vertices have distinct color codes,
then $c$ is called a locating coloring. The minimum number of colors needed in
a locating coloring of $G$ is the locating chromatic number of $G$, denoted by
$\Cchi_{{}_L}(G)$. In this paper, we study the locating chromatic number of
grids, the cartesian product of paths and complete graphs, and the cartesian
product of two complete graphs.
