When a positive integer is divided by d, the remainder is 15. When ten times of the same number is divided by d. the remainder is 6. The least possible value of d is:

16

As given, Remainder is 15 so we can say the value of d is greater than 15. Only 16 and 18 is greater than 15.

Let us try with the least of the two options

Since the minimum value for the positive number, for 15 to be remainder when divided by 16 = 31

Ten times of 31 = 310

\(\frac{310}{16}\) = 6 (remainder)

Since from there only we got the solution, we need not check for 18 as it is asked for the least value for d.

So the value of d is 16.