We can start by factoring both numbers into their prime factorizations:
$135 = 3^3 \cdot 5$
$468 = 2^2 \cdot 3^2 \cdot 13$
To find the least common multiple (LCM), we need to take the highest power of each prime factor that appears in either number. 
Thus, the LCM of 135 and 468 is $2^2 \cdot 3^3 \cdot 5 \cdot 13 = \boxed{7020}$.
The answer is: 7020
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Determine the least common multiple of 135 and 468.

### Answer:
