Write an improper fraction whose denominator is LCM of 3, 4 and 6.

Answer

To solve the problem of writing an improper fraction whose denominator is the LCM of 3, 4, and 6, we will follow these steps:

### Step 1: Find the LCM of 3, 4, and 6

To find the LCM (Least Common Multiple), we can use the method of prime factorization or division. Here, we will use the division method.

1. **Divide by the smallest prime number (2, 3, etc.) until all numbers become 1:**

- Start with the numbers: 3, 4, 6
- Divide by 3:
- 3 ÷ 3 = 1
- 4 is not divisible by 3, so it remains 4.
- 6 ÷ 3 = 2
- Now we have: 1, 4, 2

- Next, divide by 2:
- 1 remains 1.
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1
- Now we have: 1, 2, 1

- Finally, divide by 2 again:
- 1 remains 1.
- 2 ÷ 2 = 1
- Now we have: 1, 1, 1

2. **Multiply the divisors used:**
- The divisors we used are 3 and 2 (twice).
- Therefore, LCM = 3 × 2 × 2 = 12

### Step 2: Write an Improper Fraction

An improper fraction is defined as a fraction where the numerator is greater than the denominator. Since we found that the LCM of 3, 4, and 6 is 12, we need to write an improper fraction with 12 as the denominator.

1. **Choose a numerator greater than 12:**
- We can choose any number greater than 12, such as 13, 15, or 20.

2. **Write the improper fraction:**
- For example, if we choose 13 as the numerator, the improper fraction will be:
- **Improper Fraction = 13/12**

### Final Answer
The improper fraction whose denominator is the LCM of 3, 4, and 6 is **13/12** (or any other fraction like 15/12, 20/12, etc., as long as the numerator is greater than 12).

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