Let the two consecutive natural numbers be $n$ and $n+1$.
The problem states that their product is 380:
$n \times (n+1) = 380$
We need to find two consecutive natural numbers that multiply to 380. We can estimate the numbers by taking the square root of 380:
$\sqrt{380} \approx 19.49$
This suggests the numbers are close to 19.49. Let's test the consecutive natural numbers around this value:
This matches the given product.
The two consecutive natural numbers are 19 and 20.
The greater of these two numbers is 20.
This corresponds to Option A.