it can probably run but its not a supported OS for LT 2013
DarrenP
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The short answer is no. However, we will update this solution when it will be.
http://usa.autodesk.com/getdoc/id=TS19048377
This blog post also talks about it as well.
http://upandready.typepad.com/up_and_ready/2012/11/windows-8-support.html
The main issue is that Windows 8 is using a newer version of .NET (4.5) and we install .NET 4 with an Autodesk 2013 product. The Media and Entertainment products are not using the .NET framework as much so the transition to newer operating systems is not affected by this requisite.