Identify the correct set of multiples of 18 from the given options, noting that a multiple of 18 must be exactly divisible by 18 without leaving any remainder.

Introduction / Context:
This question checks the understanding of multiples and divisibility, which is a core arithmetic skill. Recognizing whether a number is a multiple of a given integer is important in topics such as least common multiples, factors, and divisibility rules. Here we are asked to determine which of the listed numbers are multiples of 18 and then choose the correct option summarizing that information.

Given Data / Assumptions:
- The base number is 18.
- The individual numbers presented are 144, 72, and 306.
- A multiple of 18 is any number that can be written as 18 * n for some integer n.
- We assume all numbers are in base ten and are positive integers.

Concept / Approach:
To determine whether a number is a multiple of 18, we can test divisibility by 18 directly or break 18 into its prime factors 2 and 9, then check divisibility by both 2 and 9. A number is divisible by 2 if it ends in an even digit and divisible by 9 if the sum of its digits is a multiple of 9. Once we confirm that each number fits these conditions, we can decide whether all, some, or none of the numbers are multiples of 18 and choose the appropriate option.

Step-by-Step Solution:
Step 1: Check 144. It is even, so divisible by 2. The sum of its digits is 1 + 4 + 4 = 9, which is a multiple of 9. Therefore 144 is divisible by both 2 and 9, hence by 18. Step 2: Check 72. It is also even. The sum of digits is 7 + 2 = 9, a multiple of 9, so 72 is divisible by 18 as well. Step 3: Check 306. It is even, ending in 6. The sum of digits is 3 + 0 + 6 = 9, which again is a multiple of 9, so 306 is divisible by both 2 and 9 and therefore by 18. Step 4: Alternatively, we can divide each number by 18 directly: 144 / 18 = 8, 72 / 18 = 4, and 306 / 18 = 17, each yielding an integer quotient. Step 5: Since all three numbers are multiples of 18, the correct statement is that all of the listed numbers are multiples of 18.

Verification / Alternative check:
We can rewrite each number explicitly as a product of 18 and an integer: 144 = 18 * 8, 72 = 18 * 4, and 306 = 18 * 17. Because all three can be expressed in this way, they all qualify as multiples of 18. This matches the earlier divisibility tests and confirms that the correct option is the one stating that all of the above numbers satisfy the condition.

Why Other Options Are Wrong:
Option 144: Selecting this alone would ignore the fact that 72 and 306 are also multiples of 18.
Option 72: Similarly, choosing only 72 fails to recognize that 144 and 306 also meet the divisibility requirement.
Option 306: Picking only 306 is incorrect because 144 and 72 have already been shown to be multiples of 18.
Option None of these: This would mean none of the numbers are multiples of 18, which contradicts our calculations.

Common Pitfalls:
A common mistake is to check only divisibility by 2, forgetting the factor of 9, or vice versa. Some students also miscalculate the digit sum or misperform the division by 18. Using both the factor method (2 and 9) and direct division can help confirm the result. Another pitfall is to assume that only one option can be correct in questions where sometimes all given values satisfy the condition.

Final Answer:
All of the given numbers 144, 72, and 306 are multiples of 18, so the correct option is All of the above.