We can find the prime factorizations of 135 and 468:
\[135 = 3^3 \cdot 5 \quad \text{and} \quad 468 = 2^2 \cdot 3^2 \cdot 13.\]
The least common multiple (LCM) is the product of the highest power of each prime that appears in the factorizations. Therefore, 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:
