The Answer Is At Least 1

How many positive integers \(m\) are there, such that for some triple of positive integers \( (a, b, c) \), we have

\[ m = \frac{ a}{b} + \frac{b}{c} + \frac{c}{a}? \]


For example, if \( a = b = c \), then we get the value \( \frac{1}{1} + \frac{1}{1} + \frac{1}{1} = 3 \).

Hence, the answer is "at least 1", which applies to all 4 options. You need to figure out which is correct.

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