At a minimum how many NICs must a machine have to host virtual machines?

A single physical NIC is sufficient because virtualization platforms can create a virtual switch that connects to the physical NIC. This virtual switch then allows the host operating system and multiple virtual machines to share the single physical network adapter for external network connectivity.

While it is a common best practice to have separate NICs for management and VM traffic, it is not a minimum requirement; a single NIC can be shared for both.

Three NICs for each virtual machine is an excessive and incorrect minimum requirement; virtual machines typically share physical NICs.

Two NICs for each virtual machine plus one for management is also an excessive and incorrect minimum requirement, as virtual machines can share physical NICs and a single NIC can handle management traffic.