# Swati's Secret Number

**Discrete Mathematics**Level 4

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.