Find the least common multiple. \( 3 r^{2}, 65 r^{5} \) Write your answer as a constant times a product of single variables raised to exponents.

The least common multiple (LCM) of the two expressions \( 3r^{2} \) and \( 65r^{5} \) can be found by determining the LCM of the constants and the variables separately. 1. **LCM of the Constants:** - The constants are 3 and 65. - \( 65 = 5 \times 13 \) - Since 3 is a prime number and does not divide 65, the LCM of 3 and 65 is: \[ 3 \times 5 \times 13 = 195 \] 2. **LCM of the Variables:** - The variables are \( r^{2} \) and \( r^{5} \). - The LCM is the variable raised to the highest power: \[ r^{5} \] 3. **Combine the Results:** - Multiply the LCM of the constants by the LCM of the variables: \[ 195 \times r^{5} = 195r^{5} \] **Final Answer:** \[ \boxed{195\, r^{5}} \]