The Moon doesn't really "go round" Earth in the way a car goes round a track. It orbits Earth. To answer your question directly, the Moon completes one orbit around Earth approximately every 27.3 days. This is called a sidereal month.

However, because the Earth is also moving around the Sun, it takes about 29.5 days for the Moon to return to the same position relative to the Sun. This is called a synodic month, and it's what determines the length of a lunar month.