https://file.aiquickdraw.com/mathbot/file/1727345367327l82uzogm.jpg

The image contains the following mathematical expressions in Malayalam:

\[ 2^3 \times 3^2 \, \text{and} \, 2^2 \times 3^3 \, \text{എന്ന്} \, \text{സംഖ്യകളുടെ} \, \text{ലസാഗു} \, \text{എന്ത്?} \]

This translates to:

**What is the LCM (Least Common Multiple) of the numbers \( 2^3 \times 3^2 \) and \( 2^2 \times 3^3 \)?**

Let’s find the LCM of these two numbers.

1. The first number is \( 2^3 \times 3^2 = 8 \times 9 = 72 \).
2. The second number is \( 2^2 \times 3^3 = 4 \times 27 = 108 \).

### Prime Factorization:
- \( 72 = 2^3 \times 3^2 \)
- \( 108 = 2^2 \times 3^3 \)

### Finding the LCM:
The LCM is found by taking the highest power of each prime factor that appears in the factorizations:
- For \( 2 \), the highest power is \( 2^3 \).
- For \( 3 \), the highest power is \( 3^3 \).

Thus, the LCM is:
\[
LCM = 2^3 \times 3^3 = 8 \times 27 = 216
\]

The LCM of \( 72 \) and \( 108 \) is **216**.

Would you like more details or have any other questions?

Here are some related questions:
1. How do you calculate the LCM of more than two numbers?
2. What is the difference between LCM and HCF (Highest Common Factor)?
3. How can prime factorization help in finding the LCM?
4. Can LCM be found using the division method?
5. How do LCM and HCF apply in real-world problems?

**Tip:** Always use prime factorization to simplify the process of finding the LCM, especially for large numbers.

2^3 × 3^2, 2^2 × 3^3 എന്നി സംഖ്യകളുടെ ലസാഗു എന്ത്?

Learn how to find the LCM of the numbers 2^3 × 3^2 and 2^2 × 3^3 using prime factorization. Detailed steps provided for Grades 7-9, including prime factor powers and LCM calculation.

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