Which Mac laptop do you have?
The various Macbook models (regular Macbook, Macbook Pros, Macbook Air) have different video output jacks depending on what generation it is. Some have a miniDVI port, some have a miniDisplayPort, and some of the much older ones have a full-size DVI port, and some MB Airs have microDVI. They all need different adapters to connect to that LG monitor you got.
You need to find out which Macbook you got, so you don't end up buying the wrong adapter that won't fit your particular Macbook.