Consider the following statements: I. Two consecutive natural numbers are always co-prime. II. If m and n are relatively prime, then m × n is always even. Which of the statements given above is/are correct?

Statement I: Any two consecutive natural numbers n and n+1 have HCF 1, since any common divisor must divide their difference 1. So I is correct. Statement II: If m and n are coprime, m × n need not be even. For example, m = 3 and n = 5 are coprime, but 3 × 5 = 15 is odd. So II is false. Only I is correct.