  In the present paper, we canonically quantize an homogeneous and isotropic
Ho\v{r}ava-Lifshitz cosmological model, with constant positive spatial sections
and coupled to radiation. We consider the projectable version of that
gravitational theory without the detailed balance condition. We use the ADM
formalism to write the gravitational Hamiltonian of the model and the Schutz
variational formalism to write the perfect fluid Hamiltonian. We find the
Wheeler-DeWitt equation for the model, which depends on several parameters. We
study the case in which parameter values are chosen so that the solutions to
the Wheeler-DeWitt equation are bounded. Initially, we solve it using the {\it
Many Worlds} interpretation. Using wavepackets computed with the solutions to
the Wheeler-DeWitt equation, we obtain the scalar factor expected value
$\left<a\right>$. We show that this quantity oscillates between finite maximum
and minimum values and never vanishes. Such result indicates that the model is
free from singularities, at the quantum level. We reinforce this indication by
showing that by subtracting one standard deviation unit from the expected value
$\left<a\right>$, the latter remains positive. Then, we use the {\it
DeBroglie-Bohm} interpretation. Initially, we compute the Bohm's trajectories
for the scale factor and show that they never vanish. Then, we show that each
trajectory agrees with the corresponding $\left<a\right>$. Finally, we compute
the quantum potential, which helps understanding why the scale factor never
vanishes.
