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Wash the fireplace down with an all purpose cleaner. Some all purpose cleaners are Mr. Clean Multi-Surface Cleaner and Goo Gone All Purpose Cleaner. Spray on the cleaner and use a sponge to scrub off the buildup. After doing an initial scrubbing, switch to a mild soap. Mix the mild soap with water. Continue to scrub at the stone. Switch back to the all purpose cleaner after you've scrubbed for with the mild soap. Scrub for a while and then switch back to the mild soap if necessary. Continue switching back and forth until you are satisfied with the outcome. Allow a few minutes for the stone to dry.
Use an all purpose cleaner. Switch to mild soap. Use more all purpose cleaner.