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: Find the Prime Factorization of Each Number

#### Prime Factorization of 28
1. Start with 28.
2. 28 can be divided by 2 (the smallest prime number):
   \[
   28 \div 2 = 14
   \]
3. 14 can also be divided by 2:
   \[
   14 \div 2 = 7
   \]
4. 7 is a prime number, so we stop here.

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

The factor tree for 28 is:

```
    28
   /  \
  2    14
      /  \
     2    7
```

#### Prime Factorization of 24
1. Start with 24.
2. 24 can be divided by 2:
   \[
   24 \div 2 = 12
   \]
3. 12 can also be divided by 2:
   \[
   12 \div 2 = 6
   \]
4. 6 can be divided by 2:
   \[
   6 \div 2 = 3
   \]
5. 3 is a prime number, so we stop here.

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

The factor tree for 24 is:

```
    24
   /  \
  2    12
      /  \
     2    6
         / \
        2   3
```

### Step 2: Find the LCM Using the Prime Factorization

The LCM is found by taking the highest power of each prime factor that appears in the factorizations of both numbers.

- **For 2:** The highest power is \( 2^3 \) (from 24).
- **For 3:** The highest power is \( 3^1 \) (from 24).
- **For 7:** The highest power is \( 7^1 \) (from 28).

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

### Conclusion

The LCM of 28 and 24 is **168**.

---

Do you want more details or have any questions? Here are some related questions you might consider:

1. What is the LCM of 18 and 30?
2. How do you find the GCD of two numbers using prime factorization?
3. What is the relationship between LCM and GCD of two numbers?
4. Can you find the LCM of three numbers using prime factorization?
5. What is the difference between LCM and HCF (Highest Common Factor)?
6. How can you find the LCM using the division method?
7. How do you apply LCM in solving word problems involving multiples?
8. What are the applications of LCM in real life?

**Tip:** Always break down numbers into their prime factors when calculating the LCM or GCD; it simplifies the process!

Learn how to find the Least Common Multiple (LCM) of 28 and 24 using prime factorization. This detailed step-by-step solution includes the factor trees for both numbers and explains the method to determine LCM by taking the highest powers of common prime factors. Suitable for students in Grades 6-8.

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