The LCM of 24,48,96 and 60 would be

Options

A. 440
B. 480
C. 465
D. 484

Answer

To find the LCM (Least Common Multiple) of the numbers 24, 48, 96, and 60, we can follow these steps:

### Step 1: Prime Factorization
First, we need to find the prime factorization of each number.

- **24**:
- 24 = 2 × 12
- 12 = 2 × 6
- 6 = 2 × 3
- So, 24 = \(2^3 \times 3^1\)

- **48**:
- 48 = 2 × 24
- 24 = 2 × 12
- 12 = 2 × 6
- 6 = 2 × 3
- So, 48 = \(2^4 \times 3^1\)

- **96**:
- 96 = 2 × 48
- 48 = 2 × 24
- 24 = 2 × 12
- 12 = 2 × 6
- 6 = 2 × 3
- So, 96 = \(2^5 \times 3^1\)

- **60**:
- 60 = 2 × 30
- 30 = 2 × 15
- 15 = 3 × 5
- So, 60 = \(2^2 \times 3^1 \times 5^1\)

### Step 2: Identify the Highest Powers of Each Prime
Next, we take the highest power of each prime factor from the factorizations:

- For \(2\): The highest power is \(2^5\) (from 96).
- For \(3\): The highest power is \(3^1\) (common in all).
- For \(5\): The highest power is \(5^1\) (from 60).

### Step 3: Calculate the LCM
Now, we can calculate the LCM by multiplying these highest powers together:

\[ \text{LCM} = 2^5 \times 3^1 \times 5^1 \]

Calculating this step-by-step:

- \(2^5 = 32\)
- \(3^1 = 3\)
- \(5^1 = 5\)

Now multiply these together:

\[ \text{LCM} = 32 \times 3 \times 5 \]

Calculating \(32 \times 3\):

\[ 32 \times 3 = 96 \]

Now multiply \(96 \times 5\):

\[ 96 \times 5 = 480 \]

Thus, the LCM of 24, 48, 96, and 60 is **480**.

### Final Answer
The LCM of 24, 48, 96, and 60 is **480**.

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