According to the earth science reference tables, during which geologic time period were the continents of north america, south america, and africa closest together?

The correct answer is - Permian.

The continents of North America, South America, and Africa were all once part of a supercontinent called Pangaea. These three were all merged together during the existence of Pangaea.

That supercontinent formed around 335 million years ago, and broke apart around 175 million years ago. The peak of Pangaea was in the Permian period, and the mentioned continents were the closest to one another in that period of the geologic time scale.

With the end of the Permian, big geologic activities started, which slowly started to move the crustal plates of these three continents from one another. Because the geologic activity was continuing in the next period, North America, South America, and Africa broke apart from each other, which also marked the end of the supercontinent. While North America moved away from these two and remained a part of Laurasia for some time, Africa and South America remained attached for few more million years, while they were part of Gondwanaland.