<s>[INST] The provided code snippet is supposed to compute the dot product of two vectors. However, there's an issue with it. The code will not work correctly if the vectors have a different lengths. 

```python
def compute_dot_product(vector1, vector2):
    dot_product = 0
    for i in range(len(vector1)):
        dot_product += vector1[i] * vector2[i]
    return dot_product
```

Let's assume that we cannot use any external libraries or modules for this task. How can you modify the code so that it correctly handles vectors with different lengths?[/INST]