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Question

If for a positive integer a,aN={ax:xN} and 13N7N=kN, then the value of k is

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Solution

13N={13x:xN} ={13,26,39,}
Collection of multiples of 13

Similarly, 7N={7x:xN}
={7,14,21,}
Collection of multiples of 7

So, 13N7N contains multiples common to both 7 and 13.
i.e., 13N7N Collection of multiples of 91.
13N7N={91x:xN}=91N

Hence, k=91

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