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.

Question

UpStudy AI · Accepted Answer

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.

Write your answer as a constant times a product of single variables raised to exponents.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions

Find the least common multiple. Write your answer as a constant times a product of single variables raised to exponents.