There was a time with Lightroom v4, 5 and maybe 6, that you could extract the Serial Number in Windows, as follows-
Go to C:\ProgramData\Adobe\Lightroom and open the .lrreg file with a text editor such as Notepad and retrieve the serial number. You will have to change your file preferences in Windows so that you can see hidden folders in order to get access.
Installing v6 should be done without Creative Cloud Desktop App installed, for the Serial Number to 'work'. Also, if you purchased v6 as an 'upgrade' you would also need the v5 Serial Number.