# Swati's Secret Number

Swati made a list of $$N$$ different positive integers, each strictly less than 1000. Swati told her friend Roma what the value of $$N$$ was, and based on this value, Roma knew that there were some two integers in Swati's list whose product was divisible by 15. What is the smallest value that $$N$$ could have been?

Details and assumptions

Roma only knows that value of $$N$$. He doesn't know what the entire list is. For example, if $$N=4$$, the list could have been the numbers $$\{1, 23, 456, 789 \}$$. In this case, he can't find 2 numbers whose product is divisible by 15. Hence the answer is not 4.

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