Coprime Period

$\large\underbrace{0,1,0,1,0,0,0,1,0,1}_{\text{period}}, 0,1,0,1,0,0,0,1,0,1,0,\dots$ Let $n$ be a positive integer, and let the function $f_n:\ \mathbb N \to \{0,1\}$ be defined by $f_n(m) = \begin{cases} 0 & \gcd(n,m) > 1 \\ 1 & \gcd(n,m) = 1. \end{cases}$ That is, $f_n(m)$ tells us whether $m$ is coprime to $n$ or not. If we write out the values of $f_n,$ we get a periodic (repeating) pattern. For instance, the list above gives the values of $f_{10}$ starting at $m = 0$; the pattern repeats itself with period 10.

Consider the function $f_{1400}$. What is its period?

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Note: The period is defined as the smallest possible value, that is, the least positive $T$ such that $f_n(m + T) = f_n(m)$ for all integers $m$.