Is there a way to find the native resolution of an LCD monitor (without looking up the specs)?

"Usually a properly configured graphics card won't allow you (by default, anyway) to set a resolution higher than the maximum for the monitor, assuming that it can detect it.

Otherwise, just keep jacking up the res until you find one (of the appropriate aspect ratio) that doesn't work. You're unlikely to damage an LCD simply by briefly switching to an out-of-bounds res."

Maybe you could try Speccy. This is a great system information tool. I don't know if it tells you also possible resolutions (not installed at work).