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How many numbers can be divided by both $$3$$ and $$5$$ from $$50$$ to $$500$$? 
Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
There are $$33$$ from $$1$$ to $$500$$.  Remove number "$$15$$" and "$$30$$", thus $$33-2=31$$ 