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.

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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:**
$$
45\,x\,y\,z
$$
The least common multiple of $$ 9xy $$ and $$ 15yz $$ is $$ 45xyz $$.

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.

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