In this case, we have homomorphisms from $G$ to both $Z_{10}$ and $Z_{15}$. Let these homomorphisms be denoted by $\phi_1: G \to Z_{10}$ and $\phi_2: G \to Z_{15}$.
Now, let's consider the orders of the groups involved. We know that $|Z_{10}| = 10$ and $|Z_{15}|
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