the smallest integer is 15
note that consecutive integers have a difference of 1 between them
let the smallest integer be n
then : n, n+ 1, n + 2, n + 3, n + 4, n + 5, n + 6
are seven consecutive integers with n + 6 being the largest, thus summing gives
7n + 21 = 6(6 + n)
7n + 21 = 36 + 6n ( distributing right side )
7n - 6n + 21 = 36 ( subtracting 6n from both sides )
n + 21 = 36 ⇒ n = 36 - 21 = 15
the smallest integer is 15