Question

If a $N=\{ax;xϵN\}$, description of the set $3N\cap 7N$ is 3kN .Find k ?

Answer 1

$aN=\{an:n\in N\}=\{a,2a,3a,4a,...\}$
$\therefore 3N=\{3,6,9,12,15,18,21,24,27,30,...\}and7N=\{7,14,21,28,35,42,...\}$
$\therefore 3N\cap 7N=\{21,42,63,84,...\}=\{1\times 21,2\times 21,3\times 21,4\times 21,...\}=\{21n:n\in N\}$

$3kN=21N$

$k=7$