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 will use the prime factorization method. Here’s a step-by-step solution:

### Step 1: Prime Factorization of Each Number
- **24**:
- 24 = 2 × 12
- 12 = 2 × 6
- 6 = 2 × 3
- Therefore, 24 = 2^3 × 3^1

- **48**:
- 48 = 2 × 24
- 24 = 2^3 × 3^1 (from above)
- Therefore, 48 = 2^4 × 3^1

- **96**:
- 96 = 2 × 48
- 48 = 2^4 × 3^1 (from above)
- Therefore, 96 = 2^5 × 3^1

- **60**:
- 60 = 2 × 30
- 30 = 2 × 15
- 15 = 3 × 5
- Therefore, 60 = 2^2 × 3^1 × 5^1

### Step 2: Identify the Highest Powers of Each Prime Factor
Now, we will 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 multiply these highest powers together to get the LCM:
- LCM = 2^5 × 3^1 × 5^1
- LCM = 32 × 3 × 5

### Step 4: Perform the Multiplication
Now we will perform the multiplication:
- First, calculate 32 × 3 = 96
- Then, calculate 96 × 5 = 480

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

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