A serial number is like a car key. You should not lose it.
But I'm pretty sure you can either fetch it from your Adobe account or from an Adobe employee when contacting support.
You do not use your cc serial number for anything. CC products are activated and deactivated by your sign in with an Adobe account that has a subscription using its User ID and Password. Gone are the days you needed to enter some un-godly 20 digit serial number.
For example if your install of Photshop CC is not Activated. Use Photoshop menu Help>Sign In... Once you sing in with an account with a subscription if there is an available activion left Photoshop will becoma Activated. The you can use Photoshop's menu Help>Systen info... Looks like this you can see your accounts serial number in there.
Adobe Photoshop Version: 2014.0.0 20140508.r.58 2014/05/08:23:59:59 x64
Operating System: Windows 7 64-bit
Version: 6.1 Service Pack 1
System architecture: Intel CPU Family:6, Model:13, Stepping:7 with MMX, SSE Integer, SSE FP, SSE2, SSE3, SSE4.1, SSE4.2, HyperThreading
Physical processor count: 12
Logical processor count: 24
Processor speed: 1995 MHz
Built-in memory: 40886 MB
Free memory: 33404 MB
Memory available to Photoshop: 37129 MB
Memory used by Photoshop: 70 %
License Type: Subscription
Serial number: "your 20 digit serial number"