13N={13x:x∈N} ={13,26,39,…}
Collection of multiples of 13
Similarly, 7N={7x:x∈N}
={7,14,21,…}
Collection of multiples of 7
So, 13N∩7N contains multiples common to both 7 and 13.
i.e., 13N∩7N→ Collection of multiples of 91.
∴13N∩7N={91x:x∈N}=91N
Hence, k=91