Question 1210181
Let's break down this problem.

**Understanding the Pattern**

* **3 x 5 Rectangle:**
    * The ant travels 3 units horizontally and 5 units vertically.
    * The number of squares crossed is 3 + 5 - gcd(3, 5) = 8 - 1 = 7.
    * gcd(3,5) is the greatest common divisor of 3 and 5.

* **Generalizing the Pattern:**
    * For an m x n rectangle, the number of squares crossed is m + n - gcd(m, n).

**Applying the Pattern to the 15 x 16 Rectangle**

* **15 x 16 Rectangle:**
    * The ant travels 15 units horizontally and 16 units vertically.
    * gcd(15,16) = 1. since 15 and 16 are relatively prime.
    * The number of squares crossed is 15 + 16 - gcd(15, 16) = 15 + 16 - 1 = 30.

**Therefore, the ant will cross through 30 squares in a 15 x 16 rectangle.**