Product of two co-prime numbers is 117. Then their LCM is:

Options

A. 117
B. 9
C. 13
D. 39

Answer

To solve the problem, we need to find the LCM of two co-prime numbers whose product is given as 117.

### Step-by-Step Solution:

1. **Understanding Co-prime Numbers**:
Co-prime numbers are two numbers that have no common factors other than 1. This means their highest common factor (HCF) is 1.

2. **Given Information**:
We are given that the product of two co-prime numbers is 117. Let's denote these two numbers as \( a \) and \( b \). Therefore, we have:
\[ a \times b = 117 \]

3. **Finding the LCM of Co-prime Numbers**:
The formula for the LCM (Least Common Multiple) of two numbers \( a \) and \( b \) is given by:
\[ \text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)} \]
Since \( a \) and \( b \) are co-prime, their HCF is 1. Thus, the formula simplifies to:
\[ \text{LCM}(a, b) = \frac{a \times b}{1} = a \times b \]

4. **Calculating the LCM**:
Substituting the product of \( a \) and \( b \) into the LCM formula, we have:
\[ \text{LCM}(a, b) = 117 \]

5. **Conclusion**:
Therefore, the LCM of the two co-prime numbers is:
\[ \text{LCM} = 117 \]

### Final Answer:
The LCM of the two co-prime numbers is **117**.

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