For Japan you need at least a 120-hour TEFL with 6 hours practicum (TEFL certificates below 120 hours require 3 months experience), CELTA, DELTA, or Trinity certTESOL. You also need a bacheler's degree in any field, and provide a criminal background check.
As I understand it, it would depend on which country you are travelling to. Assuming that you meet the job criteria (CELTA, degree etc.) I would imagine that the youngest would be the minimum necessary to get a work visa for whichever country you are applying to work in (generally 18).
For Japan you need at least a 120-hour TEFL with 6 hours practicum (TEFL certificates below 120 hours require 3 months experience), CELTA, DELTA, or Trinity certTESOL. You also need a bacheler's degree in any field, and provide a criminal background check.