Will a 240HZ monitor work with any computer?

I have a Lenovo Gaming desktop and it's extremely powerful but my 60Hz monitor is my limit. Would a 240Hz monitor actually work with my computer? Will I see a smoother framerate? Or will the computer only output 60fps on the 240Hz monitor. Or will it just output what ever the game is programmed to output.

If the monitor drivers are installed and if the monitor is detected correctly, it should run up to 240Hz or FPS. This is also dependent on graphics settings and computer performance.

It should work with most computers its just down to if the graphics card can pump out that much framrate