TV as Computer Monitor. Why no 1080p?

I recently built my own gaming rig. To save some coin I just have it hooked up to a 32 " LCD I used to watch movies and play 360. The weird part is that when I used my xbox or my home theatre system, the TV displayed in 1080p with no issues. Now I'm running an HDMI from my computer to the TV and my computer is telling me that the native resolution is 1366 x 768. And I'm pretty sure its analyzing the screen correctly because it even knows its an LG. But if I crank it up to 1920 x 1080 or whatever the max size for 16:9 is, it doesnt fit.

I hope the combined knowledge of Tom's Hardware can enlighten me on this matter.

Thanks