A pendulum clock that maintains the correct time on the earth is...

The time period of a simple pendulum is given by $T = 2\pi \sqrt{\dfrac{l}{g}}$.

The acceleration due to gravity on the moon is $g_m = \dfrac{g_e}{6}$.

The time period on the moon is $T_m = 2\pi \sqrt{\dfrac{l}{g_m}} = 2\pi \sqrt{\dfrac{6l}{g_e}} = \sqrt{6} T_e$.

Since the time period increases by a factor of $\sqrt{6}$, the pendulum takes $\sqrt{6}$ times longer to complete one oscillation.

Thus, the clock runs $\sqrt{6}$ times slower on the moon.