Give me the driving distance from Limerick to the Cliffs of moher
Googlemaps will give you the driving distance (use the 'Directions' option) as will this reliable UK & Ireland website, which is my preferred option when researching trips in either country:
The AA site will gives a detailed route (printable), route info and route options such as 'avoid motorways' (the fastest route for this trip includes a section on the M18).
Limerick City > Cliffs of Moher is roughly 50 miles. It should take you roughly 1.5 hours, as long as there is no extra traffic congestion, heavy rain (which always slows traffic) or slow-moving vehicles (tractor, coach, truck etc) which you cannot pass.