It does sound rather odd, but it is actually correct. Imagine that you are using a car to travel through the desert. On most compact cars (in the US, anyway) the fuel tank is 10-12 gallons (~37 - ~45 litres.) Generally speaking, this is enough to travel ~350 miles (560 km.) Thus, the maximum amount of fuel will take the car a certain distance.
But let us say that the desert is 500 miles (800 km) across, with no fueling stations anywhere in that distance. The maximum amount of fuel the car can hold will not be enough to make it across.
Therefore, in order to have even a chance of successfully crossing the desert, the car's maximum amount of fuel must be at least 15 gallons (55 litres.) If the maximum does not meet this minimum standard, the car does not have even the possibility of a successful crossing.
Because of the confusion that can result from this sentence construction, it's usually better to phrase it something like this:
The maximum must be larger/greater than. . .