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quotient module $\mathbb{Z}^3/(2,0,3)\mathbb{Z}$

Is $\mathbb{Z}^n/(m,a_2,...,a_2)\mathbb{Z}\cong\mathbb{Z}/m\mathbb{Z}\oplus\mathbb{Z}^{n-1}$ for $0<m<a_2,...,a_n\in\mathbb{Z}$ (as $\mathbb{Z}$-modules)? If not, how can you compute something ...
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