You're asking for the smallest distance between two things, but you've given me two very different units of measurement. Here's how to break it down:

* Earth to Moon: The average distance between Earth and the Moon is about 238,855 miles (384,400 kilometers). This distance varies slightly depending on the Moon's position in its orbit.

* Light-Year: A light-year is the distance light travels in one year, which is roughly 5.88 trillion miles (9.46 trillion kilometers).

The smallest distance is clearly the distance between Earth and the Moon. A light-year is vastly larger than the distance to the Moon.

To put it in perspective, the distance to the Moon is about 1/300,000th of a light-year.