Which of these is a valid Roman numeral? Support your answer with reason in each case.
LCCXXIII

Answer

To determine whether "LCCXXIII" is a valid Roman numeral, we need to analyze the components of the numeral and the rules of Roman numeral formation.

### Step-by-Step Solution:

1. **Identify the Roman Numerals**:
- The given numeral is "LCCXXIII".
- Breaking it down: L = 50, C = 100, X = 10, and I = 1.

2. **Check the Order of Roman Numerals**:
- Roman numerals are typically written from largest to smallest from left to right.
- In "LCCXXIII", we have L (50), followed by two Cs (100 each), then two Xs (10 each), and three Is (1 each).

3. **Analyze the Structure**:
- According to Roman numeral rules, a smaller numeral can precede a larger numeral to indicate subtraction (e.g., IV for 4), but a larger numeral cannot precede a smaller numeral unless it is a specific case of subtraction.
- In "LCCXXIII", the C (100) follows L (50). This is acceptable, but there are two Cs in succession.

4. **Check for Valid Combinations**:
- The numeral "CC" represents 200, which is valid, but it comes after L, which already represents 50.
- According to Roman numeral rules, a numeral representing hundreds (C) should not follow a numeral representing tens (X) or units (I) without a proper structure.

5. **Conclusion**:
- The combination "LCC" is not valid because a hundred (C) cannot follow a fifty (L) without a proper structure.
- Therefore, "LCCXXIII" is not a valid Roman numeral.

### Final Answer:
"LCCXXIII" is not a valid Roman numeral because the structure violates the rules of Roman numeral formation, where a numeral representing hundreds cannot follow a numeral representing tens or units without proper order.

---