Explanation:

To find the smallest integer divisible by 3, 7, and 18, we calculate the least common multiple (LCM).

- Factorize the Numbers:

- 3 = 3

- 7 = 7

- 18 = 2 × 3²

- LCM Calculation:

- The LCM must include all unique prime factors at the highest power found in any of the numbers.

- Therefore, LCM = 2 × 3² × 7 = 126.

Let's review the options:

- Option 1: 63: Only divisible by 3 and 7, not by 2.

- Option 2: 252: Divisible by all, but not the smallest.

- Option 3: 72: Only divisible by 3 and 2, not by 7.

- Option 4: 126: Divisible by 3, 7, and 18.