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The smallest number greater than $2$ that leaves a remainder of $2$ when divided by $3,4,5$, or $6$ lies between what numbers? (2012 AMC 8 Problem, Question \# 15) 
Overseas Competition->Knowledge Point->Number Theory Modules
First, list number that leaves a remainder of $2$ when divided by $6$: $8,14,20,26,32,38,44,50,56,62\cdots $. Meanwhile, divide each number with $5$ to see it the number meets the condition. If the number divided by $5$ leaves a remainder of $2$, divide it by $4$ see if it still works. 