Eddie has some baseball cards from the $$1920$$s. If he divides the number of cards he has by $$4$$, then he will have $$3$$ remaining cards; if he divides the number of cards he has by $$5$$, he will have $$4$$ remaining cards; if he divides the number of cards he has by $$7$$, he will have $$6$$ remaining cards. How many cards does Eddie have at least? 
Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
The number of cards after adding $$1$$ is divisible by $$4$$, $$5$$, and $$7$$. Since the least common multiple of $$4$$, $$5$$, and $$7$$ is $$4\times5\times7=140$$, Eddie has $$140-1=139$$ cards at least. 