 
Find the LCM of the following numbers 36, 60, 48 by the common division method .

To find the Least Common Multiple (LCM) of 36, 60, and 48 using the common division method, we follow these steps:

### Step-by-Step Process:

1. **List the numbers**: We have 36, 60, and 48.

2. **Divide by the smallest prime number**: Find a prime number that divides at least one of the numbers. Keep dividing until none of the numbers can be divided by that prime number.

Let's start:

\[
\begin{array}{c|ccc}
\text{Prime Divisor} & 36 & 60 & 48 \\
\hline
2 & 18 & 30 & 24 \\
2 & 9 & 15 & 12 \\
3 & 3 & 5 & 4 \\
2 & 3 & 5 & 2 \\
3 & 1 & 5 & 1 \\
5 & 1 & 1 & 1 \\
\end{array}
\]

### Step-by-Step Explanation:
- Divide by 2 (smallest prime): \(36 \div 2 = 18\), \(60 \div 2 = 30\), \(48 \div 2 = 24\).
- Divide by 2 again: \(18 \div 2 = 9\), \(30 \div 2 = 15\), \(24 \div 2 = 12\).
- Divide by 3: \(9 \div 3 = 3\), \(15 \div 3 = 5\), \(12 \div 3 = 4\).
- Divide by 2: \(3\) remains, \(5\) remains, \(4 \div 2 = 2\).
- Divide by 3: \(3 \div 3 = 1\), 5 remains, \(2\) remains.
- Divide by 5: All remaining numbers become 1.

3. **Multiply all divisors**:
   \[
   2 \times 2 \times 3 \times 2 \times 3 \times 5 = 360
   \]

### Therefore, the LCM of 36, 60, and 48 is **360**.

Would you like further details or have any questions?

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Here are 5 related questions to enhance your understanding:
1. What is the difference between LCM and GCD?
2. How do you find the LCM of two numbers using prime factorization?
3. Can the LCM of two numbers ever be smaller than both numbers?
4. How do you find the LCM of fractions?
5. What are the applications of LCM in solving real-world problems?

**Tip**: When using the common division method, always divide by the smallest prime number and proceed step by step. This ensures you get the correct LCM!

Find the LCM of the following numbers 36, 60, 48 by the common division method.

Learn how to find the Least Common Multiple (LCM) of 36, 60, and 48 using the common division method. This detailed solution demonstrates key concepts like prime factorization and multiplication of prime divisors. Perfect for Grades 6-8 students.

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