To find the Least Common Multiple (LCM) of the numbers 24, 36, and 38, we can follow these steps:

1. **Prime Factorization**:
   - 24 = 2³ × 3
   - 36 = 2² × 3²
   - 38 = 2 × 19

2. **Identify the highest powers of all prime factors**:
   - For 2: The highest power is 2³ (from 24).
   - For 3: The highest power is 3² (from 36).
   - For 19: The highest power is 19¹ (from 38).

3. **Multiply the highest powers together**:
   \[
   \text{LCM} = 2^3 \times 3^2 \times 19 = 8 \times 9 \times 19 = 72 \times 19 = 1368
   \]

So, the LCM of 24, 36, and 38 is **1368**.

Would you like more details or have any questions? Here are some related questions:

1. How do you find the LCM of three or more numbers using prime factorization?
2. What is the difference between LCM and GCD (Greatest Common Divisor)?
3. How do you find the LCM using the listing method?
4. Can the LCM of numbers ever be smaller than any of the given numbers?
5. How do you apply LCM in solving word problems involving time schedules?

**Tip**: Knowing how to find the LCM is useful when solving problems involving addition or subtraction of fractions with different denominators.

Learn how to find the Least Common Multiple (LCM) of 24, 36, and 38 using prime factorization with a step-by-step solution. Understand the highest powers of prime factors method and apply it to determine the LCM. Suitable for students in Grades 7-9 studying number theory.

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