To find the Least Common Multiple (LCM) of 600 and 128, we can use the prime factorization method. Let's break down each number into its prime factors:

1. **Prime factorization of 600:**

\[
600 = 2^3 \times 3 \times 5^2
\]

2. **Prime factorization of 128:**

\[
128 = 2^7
\]

### LCM Calculation
The LCM is found by taking the highest powers of all the prime factors that appear in either factorization. 

- For \(2\), the highest power is \(2^7\) (from 128).
- For \(3\), the highest power is \(3^1\) (from 600).
- For \(5\), the highest power is \(5^2\) (from 600).

Now, multiply these together:

\[
LCM = 2^7 \times 3^1 \times 5^2
\]

\[
LCM = 128 \times 3 \times 25 = 384 \times 25 = 9600
\]

So, the **LCM of 600 and 128 is 9600**.

Would you like further details or have any questions?

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Here are 5 related questions for further practice:
1. What is the LCM of 24 and 36?
2. How do you find the LCM using the division method?
3. What is the LCM of 18 and 45?
4. What is the relationship between LCM and GCD?
5. Can the LCM of two numbers ever be smaller than either of the numbers?

**Tip**: The LCM of two numbers is always greater than or equal to the larger of the two numbers.

Learn how to find the Least Common Multiple (LCM) of 600 and 128 through the prime factorization method. This step-by-step guide breaks down the prime factors of 600 and 128 and shows how to compute the LCM using the highest powers of each prime factor. Perfect for Grades 6-8 students studying number theory and LCM.

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