Microsoft built its empire on the PC. Its two cash cows, Windows and Office, are hard-core, old-school PC businesses.

But the PC business has grown stagnant. Microsoft’s revenues from Windows have actually been falling lately.

The growth now is in smartphones and tablets — where Microsoft is getting clobbered by Apple (obviously) and Google (whose Android mobile operating system is wildly popular).

This, as much as anything, explains why Microsoft is paying $8.5 billion for Skype, a company that lost money last year, and that most people use for free.

Skype is available on all of the big mobile operating systems. But a particularly tight, elegant integration with Microsoft’s struggling Windows Phone operating system could be a big boost.

As Om Malik, who broke the story yesterday, writes in a post this morning:

* It would give [Microsoft] a must-have application/service that can help with the adoption of the future versions of Windows Mobile operating system.

* However, the biggest reason for Microsoft to buy Skype is Windows Phone 7 (Mobile OS) … The software giant needs a competitive offering to Google Voice and Apple’s emerging communication platform, Facetime.

A few other points from around the Web:

* Skype is also a natural complement to Microsoft’s Xbox Kinect, the popular motion-capture game system. “With its camera, microphone and internet connection, Kinect is already set up for living-room videoconferencing,” FT’s Tech Hub notes

* The WSJ says Skype is Microsoft’s biggest acquisition ever. Did the company pay too much? “Hell yes,” according to TechCrunch, which reports that the second highest offer for Skype came from Google — and was only $4 billion.