I am looking for an app or web based leave/holiday system to implement for my small PM team?

Currently leave is applied, reviewed and approved on paper. I would like to introduce an electronic system so we don’t have to wait for the right people to be in the office to approve leave and we can track all leave together so we can see who in the team is planning to be off. 

This is initially for a 12 man team and in a perfect world the application would be free. 

Thanks in advance.