Find the lcm of 28 and 24 using factor tree

To find the Least Common Multiple (LCM) of 28 and 24 using a factor tree, we need to follow these steps:

### Step 1: Prime Factorization using Factor Trees
1. **Factor Tree for 28:**
   - 28 can be factored into 2 and 14.
   - 14 can be further factored into 2 and 7.
   - The prime factorization of 28 is \(2 \times 2 \times 7 = 2^2 \times 7\).

2. **Factor Tree for 24:**
   - 24 can be factored into 2 and 12.
   - 12 can be further factored into 2 and 6.
   - 6 can be further factored into 2 and 3.
   - The prime factorization of 24 is \(2 \times 2 \times 2 \times 3 = 2^3 \times 3\).

### Step 2: List the Prime Factors
- **28:** \(2^2 \times 7\)
- **24:** \(2^3 \times 3\)

### Step 3: Find the LCM
To find the LCM, take the highest power of each prime factor present in the factorizations:
- For 2: The highest power is \(2^3\).
- For 3: The highest power is \(3\).
- For 7: The highest power is \(7\).

So, the LCM is:
\[
\text{LCM} = 2^3 \times 3 \times 7 = 8 \times 3 \times 7 = 168
\]

### Final Answer
The LCM of 28 and 24 is **168**.

Would you like more details or have any questions?

Here are some related questions:
1. What is the greatest common divisor (GCD) of 28 and 24?
2. How do you find the LCM using the GCD?
3. Can you find the LCM of three numbers using a factor tree?
4. What is the prime factorization of 84?
5. How does the prime factorization method compare to listing multiples for finding the LCM?
6. What is the smallest number divisible by both 28 and 24?
7. How do you find the LCM of 28, 24, and 18?
8. How can you use LCM in solving real-world problems?

**Tip:** When finding the LCM, always use the highest powers of all prime factors involved to ensure you cover all multiples.

Learn how to find the Least Common Multiple (LCM) of 28 and 24 using a factor tree method. Follow a detailed step-by-step guide including prime factorization and identifying highest powers of prime factors. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation