Write an improper fraction using the LCM of 14, 35, 56 as the denominator.

Answer

To solve the problem of writing an improper fraction using the LCM of 14, 35, and 56 as the denominator, we can follow these steps:

### Step 1: Find the LCM of 14, 35, and 56
To find the LCM, we can use the factorization method.

- **Factorization of 14**:
\[ 14 = 2 \times 7 \]

- **Factorization of 35**:
\[ 35 = 5 \times 7 \]

- **Factorization of 56**:
\[ 56 = 2 \times 2 \times 2 \times 7 = 2^3 \times 7 \]

### Step 2: Identify the highest powers of each prime factor
From the factorizations:
- The highest power of 2 is \(2^3\) (from 56).
- The highest power of 5 is \(5^1\) (from 35).
- The highest power of 7 is \(7^1\) (common in all).

### Step 3: Calculate the LCM
Now, we can calculate the LCM by multiplying these highest powers together:
\[ \text{LCM} = 2^3 \times 5^1 \times 7^1 = 8 \times 5 \times 7 \]

Calculating step-by-step:
- First, calculate \(8 \times 5 = 40\).
- Then, calculate \(40 \times 7 = 280\).

Thus, the LCM of 14, 35, and 56 is:
\[ \text{LCM} = 280 \]

### Step 4: Write an improper fraction using the LCM as the denominator
An improper fraction is defined as a fraction where the numerator is greater than or equal to the denominator. Since we have found that the LCM is 280, we can write an improper fraction as follows:
\[ \text{Example of an improper fraction} = \frac{281}{280} \]
or
\[ \frac{282}{280} \]
and so on.

### Final Answer
An example of an improper fraction using the LCM of 14, 35, and 56 as the denominator is:
\[ \frac{281}{280} \]

---