A gardener has a collection of flower pots. If he divides the number of flower pots by 4, he will have 3 pots remaining; if he divides the number of flower pots by 5, he will have 4 pots remaining; if he divides the number of flower pots by 7, he will have 6 pots remaining. What is the smallest number of flower pots the gardener could have? Let's think step by step and output the final answer within \boxed{}.
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