Let $r \in \mathbb { N } ^ { * }$. Let $a _ { 1 } , \ldots , a _ { r }$ be non-zero natural integers. Show that $d \left( a _ { 1 } , \ldots , a _ { r } \right)$ is the smallest non-zero natural integer that is divisible by $a _ { 1 } , \ldots , a _ { r }$.