Find the LCM of the numbers given below :
48, 64, 72, 96, 108

Answer

To find the LCM (Least Common Multiple) of the numbers 48, 64, 72, 96, and 108, we can follow these steps:

### Step 1: Find the prime factorization of each number.
- **48**:
\( 48 = 2^4 \times 3^1 \)
- **64**:
\( 64 = 2^6 \)
- **72**:
\( 72 = 2^3 \times 3^2 \)
- **96**:
\( 96 = 2^5 \times 3^1 \)
- **108**:
\( 108 = 2^2 \times 3^3 \)

### Step 2: Identify the highest power of each prime factor.
- For **2**: The highest power is \( 2^6 \) (from 64).
- For **3**: The highest power is \( 3^3 \) (from 108).

### Step 3: Multiply these highest powers together to find the LCM.
\[ \text{LCM} = 2^6 \times 3^3 \]

### Step 4: Calculate the LCM.
- First, calculate \( 2^6 \):
\[ 2^6 = 64 \]
- Next, calculate \( 3^3 \):
\[ 3^3 = 27 \]
- Finally, multiply these results:
\[ \text{LCM} = 64 \times 27 \]

### Step 5: Perform the multiplication.
\[ 64 \times 27 = 1728 \]

### Final Answer:
The LCM of 48, 64, 72, 96, and 108 is **1728**.

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