Find the least common multiple. \( 9 x y, 15 y z \) Write your answer as a constant times a product of single variables raised to exponents.

To find the least common multiple (LCM) of the expressions \( 9xy \) and \( 15yz \), follow these steps: 1. **Factor the Constants:** - \( 9 = 3^2 \) - \( 15 = 3 \times 5 \) - The LCM of the constants \( 9 \) and \( 15 \) is \( 3^2 \times 5 = 45 \). 2. **Consider the Variables:** - The variables in the expressions are \( x \), \( y \), and \( z \). - For each variable, take the highest exponent present in either term: - \( x \) has an exponent of \( 1 \) in \( 9xy \) and \( 0 \) in \( 15yz \), so use \( x \). - \( y \) appears with an exponent of \( 1 \) in both terms. - \( z \) has an exponent of \( 1 \) in \( 15yz \) and \( 0 \) in \( 9xy \), so use \( z \). 3. **Combine the Results:** - The LCM is the product of the LCM of the constants and the highest powers of each variable. - Therefore, \( \text{LCM} = 45 \times x \times y \times z \). **Final Answer:** \[ 45\,x\,y\,z \]