It is known that the sum of two natural numbers is 60, and the sum of their greatest common divisor and least common multiple is 84. What are the two natural numbers?

It is known that the sum of two natural numbers is 60, and the sum of their greatest common divisor and least common multiple is 84. What are the two natural numbers?

Let the binary number be x, y, and (x, y) = D, let x = ad, y = BD, then (a, b) = 1. According to the meaning of the title, there is a + B = 60d1 + AB = 84d, because (60, 84) = 12, so d = L, 2, 3, 4, 6, 12. When D: 1, 2, 3, 4, 6, the equations have no solution. When d = 12, the equations become a + B = 5ab = 6, the solution

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