Now, why is that so? Let's rephrase the question and analyze.
What is the minimum distance between the multiples of two number, say m and n?
- (1) Zero, if the range of the multiples is larger than the LCM of m and n. Because if the LCM is within the range then m and n both divides it, thus the distance is zero.
(2) GCD of m and n, whenever the range of multiples is less than the LCM of m and n.
Take some examples. Take integers, that will make the understanding easier.
Say, m = 3 and n = 5.
If the range of multiples is greater than 15, then 3 and 5 both divides 15 => The minimum distance is zero.
If the range of multiples is smaller than 15 => The minimum distance is = GCD(3, 5) = 1, which occurs for 9 and 10.
Say, m = 4 and n = 6.
If the range of multiples is greater than 12, then 4 and 6 both divides 16 => The minimum distance is zero.
If the range of multiples is smaller than 12 => The minimum distance is = GCD(4, 6) = 2, which occurs for 4 and 6 themselves.
Hence, the answer is B.
