What's the most efficient way to schedule a joint meeting with multiple faculties? I have the find a time slot that all faculties can attend. As everyone is very busy, I want to do it in a most efficient way, i.e. minimizing back and forth emails as much as possible.

One trick I can think of is to ask each of them "What time you CANNOT attend?" instead of the usual "What time you can attend?" That way, I'm more likely to get all the free slots and able to schedule after only 1 round of emails.

Is there any further tips? 

A big remaining obstacle is that the faculties still have to look at their calendar and write back to me all the time slots that are not free. I wonder if there's any technology (e.g. sharing a Google calendar?) that makes this process less time consuming for the faculties.
Use a polling tool, like Doodle. You create it, they fill in which times they are (not) available, and based on the results you choose a meeting time.