Will the power adapter damage my laptop if the wattage is not the same?
You CAN use a higher wattage adapter with a lower wattage laptop. Make sure that all the other specs are a match, including the voltage output of the adapter, and the size and polarity of the connector.
You CANNOT use a lower wattage adapter with a higher wattage laptop. Purchase an adapter that supports 120 watt laptops. An underpowered adapter may appear to work most of the time with a laptop that requires more power. However, it will likely not run the laptop and charge the battery at the same time. Also, when the laptop is running at full capacity, for example during computation or graphics intensive efforts, the adapter may not be able to provide enough power and the laptop could fail.