Explanation:

To find the smallest integer divisible by 3, 7, and 18:

- List of Divisors:

- 3 = \(3^1\)

- 7 = \(7^1\)

- 18 = \(2^1 \times 3^2\)

- Finding the Least Common Multiple (LCM):

- Take the highest power of each prime factor.

- LCM = \(2^1 \times 3^2 \times 7^1 = 2 \times 9 \times 7 = 126\)

- Option Analysis:

- Option 1: 63

- Divisible by 3 and 7, but not by 18.

- Option 2: 252

- Divisible by all, but not the smallest.

- Option 3: 72

- Divisible by 3 and 18, but not by 7.

- Option 4: 126

- Smallest integer divisible by 3, 7, and 18.

Correct Answer: Option 4 - 126