Emily has a collection of rare coins. If she divides the number of coins by 4, she will have 2 coins remaining; if she divides the number of coins by 5, she will have 1 coin remaining; if she divides the number of coins by 6, she will have 3 coins remaining. What is the smallest number of coins Emily could have? Let's think step by step and output the final answer within \boxed{}.
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