Explanation:

To find the least number that satisfies the given conditions:

- The number leaves a remainder of 9 when divided by 12, 15, and 27.

- Therefore, it can be expressed as 9 more than the least common multiple of these numbers.

Steps involved:

- Calculate the least common multiple (LCM) of 12, 15, and 27.

- The prime factorization of 12 is 2^2 * 3.

- The prime factorization of 15 is 3 * 5.

- The prime factorization of 27 is 3^3.

- LCM is 2^2 * 3^3 * 5 = 540.

- The least number is 540 + 9 = 549.

- The sum of the digits of 549 is 5 + 4 + 9 = 18.

- Verify that 549 is divisible by 11, which it is (the alternating sum of digits is 0, which is divisible by 11).

Option 3 is correct.

- Option 3: 18 is the correct answer.

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