In the The Nuka-Cola Challenge, Larry's employee ID number is used in the conversation with Milo, Robotic Foreman. See also What is Nuka Cola. Edit: Basically the Office Employee IDs are used to fool robots into believing you are actually an employee and not an enemy, preventing them to attack you and some times allowing you to interact with them. Same goes for the metro tickets. In some stations, you can activate robots that will enter in attack mode with anyone without a valid ticket, including you if you do not have any.