Let's look at $\langle a\rangle$ which is a cyclic group of order $6$. Hence, $\langle a\rangle = \\{a^0 = e, a^1, a^2 \cdots a^5\\}$, by the definition of $\langle a\rangle$, where $|\langle a \rangle| = 6$.
Now, the elements of this group that are also generators of the group $\langle a \rangle$ are those elements $a^m$, where $m$ is an integer, $0\lt m \lt 6$, such that $\gcd(m, 6) = 1$. In this case, that would be only those $a^m$, where $m \in \\{1, 5\\}$: we already know $a^1 = a$ is a generator, but $a^5$ generates $\langle a\rangle$ as well.
Can you generalize this for a cyclic group of order $n$? You can apply this, then, in the same manner, to $\langle b\rangle$ and $\langle c\rangle$.