Trip from LAX-PEK, PEK-HKG, then depart for the cruise in Hongkong

I'm US Citizen with a valid US Passport. I'm planning to take an Asia cruise that departs from Hongkong cruise port. I'm wondering if I can apply 72hrs free transit, if I travel as follow:

Flights with Air China:
LAX-PEK, and will spend 3 days travel in Beijing.
PEK-HKG, then will spend 2 days travel in Hongkong
Before getting to a cruise departing from Hongkong.

Do I need to apply for a travel visa for 3 days in Beijing, and 2 days in Hongkong before the cruise.

Thanks,
A.