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.