Can't find my product key for the sims 3 generations

I have recently started to re-install the sims 3 and the expansion packs to my laptop (they were all previously installed on this laptop). i have them all apart from generations registered on origin as it wouldnt allow me to register it on there, however i have all of them including generations registered on the sims 3 website. I have lost the key for generations and therefore cannot re-install it on my laptop, do you have any idea how i can recover this key?