Find the LCM for   28 and 24 showing the factor tree in the answer

To find the Least Common Multiple (LCM) of 28 and 24, we can follow these steps:

### Step 1: Prime Factorization of Each Number

**Factor tree for 28:**

- Start by dividing 28 by 2 (the smallest prime number):
  \[
  28 \div 2 = 14
  \]
- Now, divide 14 by 2:
  \[
  14 \div 2 = 7
  \]
- 7 is a prime number, so we stop here.

So, the prime factorization of 28 is:
\[
28 = 2^2 \times 7
\]

**Factor tree for 24:**

- Start by dividing 24 by 2:
  \[
  24 \div 2 = 12
  \]
- Now, divide 12 by 2:
  \[
  12 \div 2 = 6
  \]
- Divide 6 by 2:
  \[
  6 \div 2 = 3
  \]
- 3 is a prime number, so we stop here.

So, the prime factorization of 24 is:
\[
24 = 2^3 \times 3
\]

### Step 2: Identify the LCM

To find the LCM, take the highest power of each prime factor present in the factorization of both numbers:

- **For the prime factor 2:** The highest power is \(2^3\).
- **For the prime factor 3:** The highest power is \(3^1\).
- **For the prime factor 7:** The highest power is \(7^1\).

Now, multiply these together to find the LCM:
\[
\text{LCM} = 2^3 \times 3^1 \times 7^1 = 8 \times 3 \times 7 = 168
\]

So, the LCM of 28 and 24 is **168**.

### Factor Trees Summary:

- **28:** 
\[
\begin{array}{ccc}
& 28 & \\
& / & \backslash \\
14 & & 2 \\
& / & \backslash \\
7 & & 2 \\
\end{array}
\]
- **24:**
\[
\begin{array}{ccc}
& 24 & \\
& / & \backslash \\
12 & & 2 \\
& / & \backslash \\
6 & & 2 \\
& / & \backslash \\
3 & & 2 \\
\end{array}
\]

Would you like more details, or do you have any questions?

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### Further Practice Problems:

1. Find the LCM of 30 and 45 using the factor tree method.
2. Calculate the LCM of 18 and 24.
3. Determine the LCM of 40 and 56.
4. Find the prime factorization of 36 and 48, then compute the LCM.
5. Identify the LCM of 14, 21, and 28.
6. Calculate the LCM of 9 and 15.
7. Determine the LCM of 16 and 24.
8. Find the LCM of 10 and 25.

**Tip:** When finding the LCM, always ensure to use the highest powers of all prime factors involved!

Discover how to find the Least Common Multiple (LCM) of 28 and 24 using factor trees with our detailed step-by-step guide. Learn about prime factorization and how to apply it to determine the LCM. Suitable for Grades 6-8.

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