If multiplication of two co-prime numbers is 117, then its L.C.M. is :

Options

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

Answer

To solve the problem, we need to find the L.C.M. (Least Common Multiple) of two co-prime numbers whose product is 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 greatest common divisor (GCD) is 1.

2. **Given Information**:
We know that the product of the two co-prime numbers is 117.

3. **Finding the Co-prime Numbers**:
We need to find two numbers that multiply to give 117.
- The prime factorization of 117 is \( 3 \times 39 \) and \( 39 \) can be further factored into \( 3 \times 13 \).
- However, we can also express 117 as \( 9 \times 13 \) (since \( 9 = 3 \times 3 \) and \( 13 \) is prime).

4. **Identifying the Co-prime Pair**:
The two co-prime numbers we can take from the factors of 117 are \( 9 \) and \( 13 \).
- \( 9 \) has factors \( 1, 3, 9 \) and \( 13 \) has factors \( 1, 13 \).
- Since they share no common factors other than 1, \( 9 \) and \( 13 \) are co-prime.

5. **Calculating the L.C.M.**:
The L.C.M. of two co-prime numbers is simply the product of the two numbers.
- Therefore, \( \text{L.C.M.}(9, 13) = 9 \times 13 = 117 \).

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

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