How are least, lowest, and fewest used differently?

I recently wanted to ask "What is the lowest number of people?" Then I questioned whether either "What is the least number of people?" or "What is the fewest number of people?" is a superior alternative.

My guess is that the "fewest number" option is the best, grammatically speaking. Is it? In what ways are the words least, lowest, and fewest used differently?

Thank you!

Fewest number is not the best option. Few describes the thing being counted, not the number. If there are few people present, there are a small number of them.

For example:

"Our household produces the least amount of rubbish of those in our street."

"That box has the fewest items in it"

"That box has the smallest number of items in it." (or lowest number)

I would advise you to go with @nnnnnn's suggestion of 'the smallest number of people'.