Answer:
On average the Moon is 384,399 km (238,854.465 miles, 0.00257 AU) from the Earth.
At perigee (Closest) it is 362,570 km (225,290.553 miles, 0.0024 AU) from the Earth
At apogee (Furthest) is is 405,410 km (251,910.095 miles, 0.0027 AU) from the Earth.
Around 400 BCE, by observing the ratio of time it took earth's shadow to cross the moon during a lunar eclipse to the length of time of the moon's orbit, Greek astronomers worked out the distance to the moon as approximately 30 times earth's diameter.