Let $N$ be the set of all natural numbers. If $a N=\{a n: n \in N\}$ and $b N \cap c N=d N$, where $

Question

Let $N$ be the set of all natural numbers. If $a N=\{a n: n \in N\}$ and $b N \cap c N=d N$, where $a, b, c \in N$ and $b, c$ are coprimes, then

Professor PC Thomas Classes · Answer

If $b$ and $c$ are coprime, the intersection of multiples of $b$ and multiples of $c$ is multiples of $bc$. Thus $d = bc$.