If `a=xy^(2)` and `b=x^(3)y^(5)` where x and y are prime numbers then LCm of (a,b) is _____________.

Answer

To find the LCM of \( a \) and \( b \), we will follow these steps:

1. **Identify the expressions for \( a \) and \( b \)**:
- Given \( a = xy^2 \)
- Given \( b = x^3y^5 \)

2. **Determine the prime factorization of \( a \) and \( b \)**:
- The prime factorization of \( a \) is:
\[ a = x^1y^2 \]
- The prime factorization of \( b \) is:
\[ b = x^3y^5 \]

3. **Identify the highest powers of each prime factor in \( a \) and \( b \)**:
- For the prime \( x \):
- The power in \( a \) is \( 1 \)
- The power in \( b \) is \( 3 \)
- The highest power is \( 3 \), so we take \( x^3 \).

- For the prime \( y \):
- The power in \( a \) is \( 2 \)
- The power in \( b \) is \( 5 \)
- The highest power is \( 5 \), so we take \( y^5 \).

4. **Combine the highest powers to find the LCM**:
- Thus, the LCM of \( a \) and \( b \) is:
\[ \text{LCM}(a, b) = x^3y^5 \]

So, the LCM of \( a \) and \( b \) is \( x^3y^5 \).