If $a\mathbb{N}=\{ax:x\in \mathbb{N}\}$, then $2\mathbb{N}\cap 5\mathbb{N}$ is:

$a\mathbb{N}$ represents the set of all multiples of $a$.$2\mathbb{N}=\{2,4,6,8,10,12,14,16,18,20,\dots \}$$5\mathbb{N}=\{5,10,15,20,25,\dots \}$ The intersection $2\mathbb{N}\cap 5\mathbb{N}$ consists of elements that are common to both sets, which are the common multiples of $2$ and $5$.Common multiples are $\{10,20,30,\dots \}$.This set is equivalent to $10\mathbb{N}$, where $10$ is the Least Common Multiple (LCM) of $2$ and $5$.