Finding errors in my LCM proof

[Fisicks]

Unfortunately I lack the skills to type this proof up in latex but I'd really appreciate it if someone could read through my proof and finds the errors that I'm pretty sure exist lol. On a side note I know there must be an easier way to prove this problem but I'm still happy with what I've done.

Click on the image twice to blow it up so its readable!

 

[Fisicks]

Well I actually found the easier way I talked about above working on a different problem lol. If anyone read my proof up there I found that z must equal b/gcd(a,b) thus all common multiples have the form abn/gcd(a,b) as n goes from 1 to infinity.