Problem $13\mathrm{.}029-$ Gear speed in a clock

A compound reverted gear train is to be designed to provide the appropriate ratio between the minute hand and the hour hand of a clock. The hour hand is attached to the shaft of gear $5$ such that the rotational speed of the hour hand will equal the rotational speed of gear $5.$ The shaft of gear $2$ passes through the center of the hollow shaft of gear $5$ and has the minute hand attached to it$.$ Use spur gears with a $\backslash (20\mathrm{.}0^\{\backslash$circ$\}\backslash )$ pressure angle and full$-$depth teeth. Specify appropriate numbers of teeth, while minimizing the gearbox size and avoiding the interference problem in the teeth.

The number of teeth on gear $2$ is

The number of teeth on gear $3$ is

The number of teeth on gear $4$ is

The number of teeth on gear $5$ is