LCM of 14, 28, 126 and 280 is

Options

A. ` 2 xx 3 xx 5xx7 `
B. `2^(2) xx 3^(2) xx 5 xx 7`
C. `2^3 xx 3^2 xx5xx7`
D. `2xx7`

Answer

To find the Least Common Multiple (LCM) of the numbers 14, 28, 126, and 280, we can follow these steps:

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

- **14**:
- 14 = 2 × 7

- **28**:
- 28 = 2^2 × 7

- **126**:
- 126 = 2 × 3^2 × 7

- **280**:
- 280 = 2^3 × 5 × 7

### Step 2: Identify the Highest Powers of Each Prime Factor
Next, we identify the highest power of each prime factor present in the factorizations:

- For **2**: The highest power is 2^3 (from 280).
- For **3**: The highest power is 3^2 (from 126).
- For **5**: The highest power is 5^1 (from 280).
- For **7**: The highest power is 7^1 (from all numbers).

### Step 3: Multiply the Highest Powers Together
Now, we multiply these highest powers together to find the LCM:

LCM = 2^3 × 3^2 × 5^1 × 7^1

### Step 4: Calculate the LCM
Now we calculate the product:

- 2^3 = 8
- 3^2 = 9
- 5^1 = 5
- 7^1 = 7

Now, multiply these together:

1. 8 × 9 = 72
2. 72 × 5 = 360
3. 360 × 7 = 2520

Thus, the LCM of 14, 28, 126, and 280 is **2520**.

### Final Answer
The LCM of 14, 28, 126, and 280 is **2520**.

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