The smallest common multiple of 14, 28 and 56)/ 8 is equal to

Options

A. 6
B. 9
C. 7
D. 8

Answer

To find the smallest common multiple (LCM) of the numbers 14, 28, and 56, and then divide that result by 8, we can follow these steps:

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

- **14**: The prime factors are \(2 \times 7\).
- **28**: The prime factors are \(2^2 \times 7\).
- **56**: The prime factors are \(2^3 \times 7\).

### Step 2: Determine the LCM
To find the LCM, we take the highest power of each prime number that appears in the factorizations:

- For the prime number **2**, the highest power is \(2^3\) (from 56).
- For the prime number **7**, the highest power is \(7^1\) (common in all).

Thus, the LCM is calculated as follows:
\[ \text{LCM} = 2^3 \times 7^1 = 8 \times 7 = 56 \]

### Step 3: Divide the LCM by 8
Now that we have the LCM, we need to divide it by 8:
\[ \frac{\text{LCM}}{8} = \frac{56}{8} = 7 \]

### Final Answer
The smallest common multiple of 14, 28, and 56 divided by 8 is equal to **7**.

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