To solve this problem, consider five consecutive integers \( n, n+1, n+2, n+3, n+4 \). Among any set of five consecutive integers, at least one is divisible by 5, at least one is divisible by 2, and at least one is divisible by 3. This guarantees that the product is divisible by \( 5 \times 2 \times 3 = 30 \). - Appfinity Technologies