absolute, bare, very
agreed, guaranteed
recommended
federal, legal, mandatory, required, statutory
age (AmE)
Many states impose an age minimum of eighteen for the death penalty.

keep sth to, reduce sth to
Two fire crews managed to keep damage to a minimum.

reach
The sun's temperature reached a minimum in the summer of 1981.

exceed
regard sth as
A temperature of 121°C is regarded as the minimum necessary to achieve sterility.

pay
Many people pay the minimum on their credit cards.

above (the) minimum, at (a/the) minimum
Candidates must have a degree at a minimum.

below (the) minimum, down to a minimum
We tried to keep costs down to a minimum.

minimum of
a minimum of $20
a minimum of fuss

the minimum necessary, the minimum needed
the minimum possible
He's always done the minimum possible to pass his exams.

with the minimum of delay, with the minimum of disruption, with the minimum of fuss
with the minimum of effort
The tent can be put up with the minimum of effort.

with the minimum of risk

Minimum is used with these nouns:
altitude, amount, charge, delay, disruption, distance, disturbance, duration, expenditure, impact, investment, level, limit, number, payment, penalty, percentage, qualification, quantity, requirement, salary, sentence, size, standard, temperature, threshold, training, wage, width