1. **Problem:** The product of three numbers is 3876. Two of the numbers are 17 and 19. Find the third number. 2. **Formula:** If the product of three numbers $a$, $b$, and $c$ is given by $$a \times b \times c = P,$$ then the third number $c$ can be found by $$c = \frac{P}{a \times b}.$$ Important rule: Division is the inverse operation of multiplication. 3. **Calculation:** Given $a = 17$, $b = 19$, and $P = 3876$, calculate: $$c = \frac{3876}{17 \times 19}$$ First, calculate the denominator: $$17 \times 19 = 323$$ Then divide: $$c = \frac{3876}{323} = 12$$ 4. **Answer:** The third number is **12**. This matches option B.