Bad advice -(You'll need a grub product if there is more than one grub per sq foot.)
One grub per square foot is far below the action level for applying grub controls.
10 or more grubs/sq ft is more appropriate.
A good product to control Japanese beetle and a few other species of grubs is called milky spore which is a bacteria that specifically targets them. It takes a year or two to work fully as the spores reproduce inside the grubs to reinfect more grubs as long as they occur. Benneficial nematodes are another approach.
Setting your mower to cut the grass at about 3" high will do much to control weeds provided you mow often enough to keep the weeds from setting seed. Adjusting the soil pH will also allow the turgrass to outcompete the weeds. A simple pH test is cheap and many garden centers will do it free.
In the Northeast where cool season grasses tend to go dormant during the hottest part of summer the beetles prefer to lay their eggs in turf that is irrigated. Simply allowing the grass to be dormant during this peroid by suspending irrigation will send the next generation of grubs to the neighbors who irrigate during this period.