Serial Number - different user ID

Due to some issues under an old user name, I created a new user ID on my mac (OSX).  When launching Lightroom 3, it is asking for the Serial Number.  I do not have this available.  I can launch LR under the old user name without any problems, is there a way to launch under the old user name and get the SN so I can enter under the new user ID (only one computer, one OS, just different user IDs)