Note: Microsoft 365 installations don’t require a license key as they activate automatically when you log on to Office with your Microsoft Account.
However, for either version there is no need to completely reinstall Office. The proper method to determine or change the Product Key depends on your version of Office or Outlook. While you could simply try one of your Product/License Keys and see if it gets accepted, it’s not a very sophisticated approach. How can I find out which license I've used for which computer and how can I change the key if needed? I've got several licenses for Office and Outlook but I'm not sure which one which ones I've used and which ones are free.