If ${\mathrm{N}}_{\mathrm{a}}=\{\text{ an }:\mathrm{n}\in \mathrm{N}\}\text{ and }{\mathrm{N}}_{\mathrm{b}}\cap {\mathrm{N}}_{\mathrm{c}}={\mathrm{N}}_{\mathrm{a}}$ where $\mathrm{a},\mathrm{b},\mathrm{c}\in \mathrm{N}$and b,c are relatively prime, then

${\mathrm{N}}_{\mathrm{b}}\cap {\mathrm{N}}_{\mathrm{c}}=$set of all natural numbers which are multiples of both b and c.
$\Rightarrow {\mathrm{N}}_{\mathrm{d}}=$set of all natural numbers which are multiples of LCM of b and c 
$\Rightarrow \mathrm{d}=\mathrm{bc}(\because$b, c are relatively prime, therefore, LCM of b and c is bc)