Jason has some baseball cards from the $$1920$$s. If he divides the number of cards he has by $$3$$, then he will have $$1$$ remaining cards; if he divides the number of cards he has by $$5$$, he will have $$3$$ remaining cards; if he divides the number of cards he has by $$7$$, he will have $$5$$ remaining cards. How many cards does Jason have at least? 
Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
The number of cards after adding $$2$$ is divisible by $$3$$, $$5$$, and $$7$$. Since the least common multiple of $$3$$, $$5$$, and $$7$$ is $$3\times5\times7=105$$, Jason has $$105-2=103$$ cards at least. 