That is not correct.
First, the synchronous speed of a motor is RPM = (60*Hz)/(number of poles/2) as LouNY's table shows.
Secondly, you have the concept of AC frequency and number of poles in a generator confused. AC at two cycles per second = 120 cycles per minute (120 Hz.) You would get 120 Hz by driving the generator head at twice the speed listed in Lou's table, so if you had an 1800 RPM engine, you would use it to drive an 8 pole head instead of a 4 pole head OR take the four pole head and increase the engine speed from 1800 to 3600 RPM. Things like this were done "back in the day" to run certain high-speed motorized equipment using AC induction motors; I have an old direct drive wood shaper with a two-pole motor designed to run at 120 Hz off of a motor-generator frequency changer to give a nominal 7200 rpm spindle speed. The motor-generator set had a four-pole 1800 rpm motor driving an 8-pole wound-rotor motor to give 120 Hz.
Third, 3600 rpm is a common speed for industrial spark-ignition (gasoline/natural gas/propane) engines, not just smaller single-cylinder ones as gasoline engines' powerbands are typically much higher than 1800 rpm. Generac uses Ford's 6.8 L V10 in many of its LPG/natural gas gen sets and this engine is rated to run at 3600 rpm. (
Ford LSG875 & WSG1068 460 and 6.8 liter engines for dry fuel applications from Powertech Engines Inc.)
Fourth, the generator head may very well run at a different RPM than the engine driving it due to speed-change gears being present between the engine and the generator head. This includes pretty much every PTO generator made.