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Lol I don't know how to make a table on this site, but I will try!
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health: __7__⊥__14___⊥__21__⊥__28_
fire: 12 ║ 24 ║ 36 ║
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There are not any common factors between 7 and 12 until they are multiplied
The health inspector and the fire inspector will visit on the same day in 84 days
Hope I helped! Comment if you have a question about my answer! :)