How to calculate the number of revolutions needed to fully draw a hypotrochoid?

Question

Mathematics

There is a parametrically given hypotrochoid (spirograph toy)
How to calculate the number of revolutions (2*Pi) required to fully draw the graph

Formula and description: Wiki

for example: Wolfram

Answer 1

The least common multiple of all factors that precede the parameter that is the argument of sines-cosines.
But this is not accurate, only intuition.