LCM of two numbers is 5775. Which of the following cannot be their HCF ?

Options

A. 175
B. 231
C. 385
D. 455

Answer

To determine which of the given options cannot be the HCF (Highest Common Factor) of two numbers whose LCM (Lowest Common Multiple) is 5775, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship Between HCF and LCM**:
The relationship between the HCF (let's denote it as H) and LCM (denote it as L) of two numbers a and b is given by:
\[ H \times L = a \times b \]
This means that the product of the HCF and LCM of two numbers equals the product of the numbers themselves.

2. **Finding the Factors of 5775**:
To find which of the given options can or cannot be the HCF, we first need to find the factors of 5775. We can start by performing prime factorization of 5775.

- Dividing by 5 (since it ends with 5):
\[ 5775 \div 5 = 1155 \]
- Dividing 1155 by 5 again:
\[ 1155 \div 5 = 231 \]
- Now, we can factor 231:
\[ 231 \div 3 = 77 \]
- Finally, factor 77:
\[ 77 = 7 \times 11 \]
- Thus, the prime factorization of 5775 is:
\[ 5775 = 5^2 \times 3^1 \times 7^1 \times 11^1 \]

3. **Identifying Possible HCFs**:
The HCF must be a divisor of the LCM (5775). Therefore, we need to check which of the given options are divisors of 5775.

4. **Checking Each Option**:
Let's check each option to see if it divides 5775 evenly:
- **Option 1: 175**
\[ 5775 \div 175 = 33 \]
(This is an integer, so 175 can be an HCF.)
- **Option 2: 231**
\[ 5775 \div 231 = 25 \]
(This is an integer, so 231 can be an HCF.)
- **Option 3: 385**
\[ 5775 \div 385 = 15 \]
(This is an integer, so 385 can be an HCF.)
- **Option 4: 455**
\[ 5775 \div 455 = 12.68 \]
(This is not an integer, so 455 cannot be an HCF.)

5. **Conclusion**:
Since 455 does not divide 5775 evenly, it cannot be the HCF of the two numbers whose LCM is 5775. Therefore, the answer is:
\[ \text{Option 4: 455} \]