Let $r \in \mathbb { N } ^ { \star }$. Let $a _ { 1 } , \ldots , a _ { r }$ be non-zero natural integers. Justify that there exists a unique natural integer $d \left( a _ { 1 } , \ldots , a _ { r } \right)$ such that
$$a _ { 1 } \mathbb { Z } \cap a _ { 2 } \mathbb { Z } \cap \cdots \cap a _ { r } \mathbb { Z } = d \left( a _ { 1 } , \ldots , a _ { r } \right) \mathbb { Z }$$