Out of a quite large set of random integer numbers, I selected only those that were multiples of M or N, and rejected the rest. In the resulting (obviously smaller) subset, 50% of the numbers were multiples of N. Curiously, M wasn't 50% of N.

What is the minimum possible pair of values for M and N? The next such pair? Are there infinite possible such pairs?

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PS. If you don't know the reason for the "Cherry picking" title, check this reference or this other one.
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PPS. And if "a quite large set" of numbers doesn't satisfy you, imagine an infinite set, with every possible integer.*

The minimum possible pair of values for M and N is (M, N) = (2, 3)

The next such pair is (M, N) = (3, 4)