RedneckDude is right, in my research I've found that these "product keys" that programs produce are just generic.  Windows 10 writes the license into the mother board.  I guess if you replace your mother board then you have a problem, but not hard drives.

I knew I liked you.....          

found this article today. perhaps it will prove useful.

http://www.thewindowsclub.com/windows-10-license-hardware-configuration

From Phoon's articled link:

"Though you can perform a clean installation of Windows 10 on these computers, you will have to upgrade in-place first. First you need to upgrade so that your device is registered with Microsoft and then later, you can clean install Windows 10 without worrying about serial key."

Thanks, Buff. 

http://www.tomshardware.com/news/microsoft-reveals-windows-10-activation,30188.html

Really odd though that on two different computers upgraded to Windows 10, that the product activation keys are exactly the same. Evidently they are only important if you have to do a clean install. 

... eh.. you don't need the product key for clean install. unless you are talking about the retail key.

bit more details

http://www.ghacks.net/2015/09/29/microsofts-official-windows-10-activation-guide/

This is correct, but only AFTER you upgrade said PC and then either roll back to your former OS and dual boot, OR reformat and then clean install 10.

But in order to clean install without a key, you must first upgrade the PC to 10.

This might help?

http://www.ghacks.net/2015/09/29/microsofts-official-windows-10-activation-guide/?_m=3n%2e0038%2e1745%2ehj0ao01hy5%2e1tbn