The difference between two natural numbers is 2, and the difference between their least common multiple and greatest common factor is 142?

The difference between two natural numbers is 2, and the difference between their least common multiple and greatest common factor is 142?


Let the greatest common factor be x, and two natural numbers be MX, NX, m, n coprime respectively
The least common multiple is mnx
mnx-x=142
(mn-1)x=142=71×2
x=2
mn-1=71
mn=72=8×9
m=8
n=9
The two natural numbers are 8 × 2 = 16, 9 × 2 = 18



The difference between two natural numbers is 2, and the sum of their greatest common factor and least common multiple is 86





It is known that the difference between two natural numbers is 2, and the difference between their least common multiple and greatest common divisor is 142


Let one of the natural numbers be x, and the other bit x + 2, (1) when (x, x + 2) = 1, [x, x + 2] = 142 + 1 = 143, and (x, x + 2) × [x, x + 2] = 1 × 143 = 11 × 13 = x × (x + 2), so x = 11, x + 2 = 13; (2) when (x, x + 2) = 2, [x, x + 2] = 142 + 2 = 144, and (x, x + 2) × [...]