The answer would be
-1 (minus one)
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-3
a negative integer
1
-1: Negative integers become smaller as their absolute value increases. Therefore, the first negative integer is the smallest. This answer assumes that -0 is excluded because 0 is neither positive nor negative.
The smallest positive integer is 1. 1 is the multiplicative identity; ie anything times 1 is itself. The greatest negative integer is the most positive negative integer which is -1. Therefore the product of the greatest negative integer and the smallest positive integer is the greatest negative integer which is -1.