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Paired number GCD and LCM (Posted on 2019-05-03)

How many ordered pairs of positive integers satisfy

gcd(m³, n²) = 2²*3²
lcm(m², n³) = 2⁴*3⁴*5⁶ ?

No Solution Yet Submitted by Danish Ahmed Khan

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Puzzle Answer

Comment 2 of 2 |

We have two ordered pairs m, n) of positive integers that satisfy the given equation. These are:

1) m= (2^2)*(3^2)*(5^3), and n=(2^1)*(3^1)

2) m= (2^2)*(3^2), and n=(2^1)*(3^1)*(5^2)

Posted by K Sengupta on 2022-05-18 23:08:34

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