For earth

$$n=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$$

For moon

$$n'=\frac{1}{2\pi}\sqrt{\frac{k}{6m}}\because g_{moon}=\frac{g}{6}$$

$$\frac{n'}{n}=\frac{1}{\sqrt{6}}\therefore n':n=1:\sqrt6$$