Let n be an integer number, the next integer number is n+1. These numbers n and n+1 are two consecutive integers.
Their sum is n+n+1=2n+1 and is greater than 16, thus
2n+1>16.
Solve this inequality:
2n>16-1,
2n>15,
n>7.5.
Since n is integer, then the smallest integer that sutisfies this inequality is 8 and the next n+1=8+1=9.
Answer: the lesser of two consecutive integers is 8.