Determine the order of the steps needed to find the LCM of 16 and 18.
1. 2small4 x 3small2
2. 2 × 2 × 2 × 2 × 3 × 3
3. 16 = 2 × 2 × 2 × 2 = 2small4
3. 18 = 2 × 3 × 3 = 2 × 3small2
4.. 2small4, 3small2
5. 144

To determine the correct order of steps needed to find the Least Common Multiple (LCM) of 16 and 18, let's break it down properly:

1. **Step 1:** Factorize the numbers.
   - 16 = 2 × 2 × 2 × 2 = \( 2^4 \)  (represented as "2small4")
   - 18 = 2 × 3 × 3 = \( 2 \times 3^2 \)  (represented as "3small2")
   *(This corresponds to steps 3 and 3 in the provided list)*

2. **Step 2:** Identify the highest powers of the prime factors.
   - The prime factors are 2 and 3.
   - Take the highest power of each factor:
     - For 2: the highest power is \( 2^4 \) (from 16).
     - For 3: the highest power is \( 3^2 \) (from 18).
   *(This corresponds to step 4 in the provided list)*

3. **Step 3:** Multiply the highest powers of the factors to get the LCM.
   - \( 2^4 \times 3^2 = 16 \times 9 = 144 \)
   *(This corresponds to steps 1, 2, and 5 in the provided list)*

### Correct order of steps:
1. Step 3 (factorizing 16 and 18)
2. Step 4 (selecting \( 2^4 \) and \( 3^2 \))
3. Step 1 (writing \( 2^4 \times 3^2 \))
4. Step 2 (multiplying \( 16 \times 9 = 144 \))
5. Step 5 (LCM = 144)

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What is the LCM of 24 and 36 using prime factorization?
2. How do you find the LCM of two numbers using their GCD?
3. Why is it necessary to take the highest powers of the prime factors when calculating the LCM?
4. Can the LCM of two numbers be smaller than either of the numbers?
5. How is the LCM useful in solving problems involving fractions?

**Tip:** The LCM of two numbers is always a multiple of both numbers.

Determine the order of the steps needed to find the LCM of 16 and 18.

Learn the step-by-step process to find the Least Common Multiple (LCM) of 16 and 18 using prime factorization. This solution explains how to break down both numbers into prime factors, identify the highest powers, and calculate the LCM. Suitable for students in Grades 6-8.

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