tile floor cleaning tips?

I have an account that has the little 2" tiles on the floor. They are green with white grout with alot of dirty foot traffic and the management wants to know how I can get them clean and keep them clean. I usually just use a neutral floor cleaner on them as well as the office floors. The only thing I've found that will really clean the tile is the magic sponge or magic eraser, but who wants to get on their hands and knees every week or so. I need something strong enough that I can just mop it clean. Any suggestions out there would be greatly appreciated. Thanks!

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