It is known that the difference between two natural numbers is 2, and the sum of their least common multiple and greatest common divisor is 42

It is known that the difference between two natural numbers is 2, and the sum of their least common multiple and greatest common divisor is 42

The greatest common divisor of these two natural numbers must be able to divide their difference, so that we can know that the greatest common divisor of these two natural numbers may be 1 or 2
If the greatest common divisor is 1, then the least common multiple is 41, and the difference between the two numbers is 2, we can see that there are no such two natural numbers
If the greatest common divisor is 2, then the least common multiple is 42-2 = 40, and the product of two natural numbers is always equal to the product of their greatest common divisor and two coprime numbers, and the difference between the two natural numbers is 2, so we can know that the two numbers are 8 and 10
The greatest common divisor of 8 and 10 is 2, the least common multiple is 40, and the sum of the least common multiple and the greatest common divisor is 42