4. Can we find two such natural numbers $x$ and $y$ that the sum of these numbers plus 2021 is less than the sum of their GCD and LCM?
Solution: In other words, we need to determine whether the equation GCD(x, y) + LCM(x, y) - (x + y) = 2021 has a solution in the set of natural numbers. Let's rewrite this equation as GCD(x, y) + LCM(x, y) + x + y = 2021. Let's analyze the obtained equation in terms of parity. If both numbers x and y are even, then their GCD and LCM are also even, and the sum of four even numbers must also be even. If they are both odd, then their GCD and LCM are odd, and the sum of four odd numbers is even. Finally, if one of the numbers x, y is even and the other is odd, then the GCD is odd and the LCM is even, and the sum is also even. Thus, such numbers do not exist.

Answer: They do not exist.