The question asks to find the Least Common Multiple (LCM) of 4, 6, and 8 using prime factorization. Here's how we can solve it:

Step 1: Prime Factorization

We first express each number as a product of prime factors:

• $4 = 2^2$
• $6 = 2 \times 3$
• $8 = 2^3$

Step 2: Identify the Highest Powers of Prime Factors

Now, for each distinct prime factor, we take the highest power that appears in any of the factorizations:

• For 2: The highest power is $2^3$ (from 8).
• For 3: The highest power is $3$ (from 6).

Step 3: Multiply the Highest Powers of Each Prime Factor

Now, we multiply the highest powers of the primes to get the LCM:

$\text{LCM} = 2^3 \times 3 = 8 \times 3 = 24$

Thus, the LCM of 4, 6, and 8 is 24.

Would you like more details on any part of this process? Here are a few follow-up questions you might find useful:

1. What is the difference between LCM and GCD (Greatest Common Divisor)?
2. Can the LCM of two numbers ever be smaller than either of the numbers?
3. What are other methods to find the LCM besides prime factorization?
4. Why is prime factorization a useful method for finding the LCM?
5. How would you find the LCM of more than three numbers?

Tip: Remember, the LCM is useful in problems where you need a common multiple of several numbers, like finding a common time for events that repeat at different intervals.