The LCM of two coprime numbers is 119. Find their HCF.

Options

A. 7
B. 17
C. 1
D. 119

Answer

To solve the problem, we need to find the HCF (Highest Common Factor) of two coprime numbers given that their LCM (Least Common Multiple) is 119.

### Step-by-Step Solution:

1. **Understanding Coprime Numbers**:
- Two numbers are said to be coprime if their only common factor is 1. This means that their HCF is 1.

2. **Given Information**:
- We are given that the LCM of the two coprime numbers is 119.

3. **Using the Relationship Between LCM and HCF**:
- There is a mathematical relationship between the LCM and HCF of two numbers:
\[ \text{LCM} \times \text{HCF} = \text{Product of the two numbers} \]
- Since the two numbers are coprime, their HCF is 1.

4. **Substituting the Values**:
- Let’s denote the two coprime numbers as \( a \) and \( b \).
- From the relationship:
\[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b \]
- Substitute the known values:
\[ 119 \times 1 = a \times b \]
- This simplifies to:
\[ a \times b = 119 \]

5. **Finding the HCF**:
- Since we established that the two numbers are coprime, their HCF is:
\[ \text{HCF}(a, b) = 1 \]

### Final Answer:
The HCF of the two coprime numbers is **1**.