As I said above in such a case you can use third-party software like ProduKey. In case if you lost it then there is no need to worry. Otherwise, if you have your old Windows 7 or 8 product key with you, then you can do the clean install on the other hardware provided you have updated your copy of installed Windows 10 to November Update or later then it. If you want to change the hardware, then you need to contact Microsoft support and notify them of the change to get your copy activated. Why it happens because the hardware is the same.
Once the process completes, a copy of Windows will activate automatically when you connect it with an internet connection. Here you have to skip the step and completes the installation. Another question is what will happens if one wants to clean install Windows 10 on the same machine? While installation, windows ask you to provide Windows 10 serial key.
So you will not find any Windows 10 product activation key.
In a case when you upgraded your PC from Windows 7, 8, 8.