To find the Least Common Multiple (LCM) of 18 and 49, we'll follow these steps:

1. **Prime factorization**:
   - 18 = 2 × 3²
   - 49 = 7²

2. **Take the highest powers of all prime factors**:
   - For 2: maximum is 2¹
   - For 3: maximum is 3²
   - For 7: maximum is 7²

3. **Multiply the highest powers together**:
   \[
   \text{LCM} = 2^1 \times 3^2 \times 7^2 = 2 \times 9 \times 49 = 882
   \]

Thus, the **LCM of 18 and 49 is 882**.

Would you like more details or have any other questions?

Here are some related questions:
1. How do you find the greatest common divisor (GCD) of 18 and 49?
2. What is the prime factorization of 18 and 49?
3. How is the LCM useful in solving fraction addition?
4. Can you find the LCM of more than two numbers, say 18, 49, and 72?
5. What is the difference between LCM and GCD?

**Tip:** The LCM helps when finding common denominators in fractions or synchronizing cycles in problems involving multiple time intervals.

Discover how to calculate the Least Common Multiple (LCM) of 18 and 49 through prime factorization. This detailed guide covers key concepts like number theory and prime factorization, providing a step-by-step solution suitable for students in Grades 6-8.

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