If you mean you purchased LR CC and are still in the middle of your annual subscription period and your current month is paid, then you can license LR by merely signing in with your Adobe ID. I think either the Help / Sign-In within LR or at least signing into the CC Desktop app will do it. If some of what I’ve said isn’t your situation or you have signed in to one or the other places, please specify.
i purchased Creative Cloud Photography plan (one-year)
I want the serial number with which I can get Lightroom to work