If a positive integer multiple of 864 is chosen randomly, with each multiple having the same probability of being chosen, what is the probability that it is divisible by 1944?
This can be easily solve by dividing out the greatest common divisor between 864 and 1944.
Since and , this problem becomes equivalent to the one of finding the probability of randomly chosen positive integer multiples of is divisible by . Since and are coprime, we only can be considered. Hence, that probability is .