If a and b are two prime numbers then find LCM (a,b)/

Answer

To find the LCM (Least Common Multiple) of two prime numbers \( a \) and \( b \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Prime Numbers**:
- Prime numbers are defined as numbers greater than 1 that have no positive divisors other than 1 and themselves.
- Examples of prime numbers include 2, 3, 5, 7, 11, etc.

2. **Identifying the LCM**:
- The LCM of two numbers is the smallest number that is a multiple of both numbers.

3. **Properties of Prime Numbers**:
- Since \( a \) and \( b \) are both prime, they do not share any common factors other than 1.
- This means that the only divisor common to both \( a \) and \( b \) is 1.

4. **Calculating the LCM**:
- For two prime numbers, the LCM can be calculated as:
\[ \text{LCM}(a, b) = a \times b \]
- This is because there are no other multiples that can be formed from \( a \) and \( b \) that are smaller than their product.

5. **Conclusion**:
- Therefore, the LCM of two prime numbers \( a \) and \( b \) is simply their product:
\[ \text{LCM}(a, b) = a \times b \]

### Final Answer:
The LCM of two prime numbers \( a \) and \( b \) is \( a \times b \).

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