Find a whole number between $$100$$ and $$200$$ that has all of the following properties.  When the number is divided by $$3$$ the remainder is $$2$$.  When the number is divided by $$5$$ the remainder is $$2$$.  When the number is divided by $$7$$ the remainder is $$2$$.  What is the number? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem->Chinese Remainder Theorem with Constant Remainder