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Let's break down the problem step by step:

We are given that:
- \( ABC \) is a three-digit number, where \( A < B < C \).
- \( B \) and \( C \) are multiples of \( A \).
- \( C \) is three more than \( B \).

We need to determine which of the provided options can be this three-digit number.

Let’s go through the possibilities by analyzing each number:

### 1. Option (A): 136
- \( A = 1 \), \( B = 3 \), and \( C = 6 \).
- Here, \( B = 3 \times A \) (so \( B \) is a multiple of \( A \)).
- \( C = B + 3 \), since \( 6 = 3 + 3 \).
- Therefore, this satisfies all conditions.

### 2. Option (B): 248
- \( A = 2 \), \( B = 4 \), and \( C = 8 \).
- Here, \( B = 2 \times A \) (so \( B \) is a multiple of \( A \)).
- \( C = B + 4 \), not \( B + 3 \) (because \( 8 - 4 = 4 \)).
- This does not satisfy the condition that \( C = B + 3 \).

### 3. Option (C): 269
- \( A = 2 \), \( B = 6 \), and \( C = 9 \).
- Here, \( B = 3 \times A \) (so \( B \) is a multiple of \( A \)).
- However, \( C = 9 \), and \( B + 3 = 9 \), so this satisfies the condition \( C = B + 3 \).
- This option works.

### 4. Option (D): 369
- \( A = 3 \), \( B = 6 \), and \( C = 9 \).
- Here, \( B = 2 \times A \) (so \( B \) is a multiple of \( A \)).
- \( C = B + 3 \), since \( 9 = 6 + 3 \).
- This satisfies all conditions.

### 5. Option (E): 447
- \( A = 4 \), \( B = 4 \), and \( C = 7 \).
- This doesn't satisfy the condition \( A < B < C \) because \( A = B \).
- This is not a valid option.

### Conclusion:
Both Option (A): 136 and Option (D): 369 satisfy the conditions of the problem. However, Option (D): 369 is the best choice because \( ABC \) must be greater than 200, and 369 fits that criteria better than 136.

So, the correct answer is **(D) 369**.

Do you want further details or have any questions?

### Here are five related questions:
1. What are the properties of multiples and how do they relate to inequalities like \( A < B < C \)?
2. How can divisibility rules help in finding numbers that satisfy multiple conditions?
3. What is the importance of step-by-step reasoning in solving word problems?
4. Can you think of other examples where one number is a multiple of another with certain conditions (like differences)?
5. How do you solve problems involving conditions on digits in a number?

### Tip:
When dealing with multiple conditions in a problem, always systematically test each condition to eliminate incorrect options easily.

ABC represents a three-digit number greater than 200, where A < B < C. If B and C are multiples of A, and C is three more than B, which of the following number can be the three-digit number ABC? (Options: 136, 248, 269, 369, 447)

Explore how to find the three-digit number ABC where A < B < C, B and C are multiples of A, and C is three more than B. This problem involves properties of numbers and inequalities, suitable for middle school students.

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