For this task, we will be using Python with Flask as the web framework. We will also use Jinja2 for HTML templating. The architecture will consist of three main files:

1. app.py: This is the main entry point of the application. It will contain the Flask application and the route for generating the random number.
2. templates/index.html: This is the HTML template that will be rendered by the Flask application. It will display the random number.
3. requirements.txt: This file will list all the Python dependencies that need to be installed for the application to run.

Let's start with the app.py file:

app.py