minimal
Representing the smallest possible amount or the least extent; very small or insignificant.
Der Unterschied zwischen den beiden Angeboten ist nur minimal.
The difference between the two offers is only minimal.

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Representing the smallest possible amount or the least extent; very small or insignificant.
Der Unterschied zwischen den beiden Angeboten ist nur minimal.
The difference between the two offers is only minimal.

The word 'minimal' belongs to an international word family derived from the Latin 'minimus' (the smallest). Words like 'Minimum' (minimum) or 'minus' (minus) have the same origin and help you understand the meaning 'very small'.
Wir sollten das Risiko so minimal wie möglich halten.
We should keep the risk as minimal as possible.
'Minimal' (minimal) can also be used like an adverb to modify another adjective or a verb. It then means 'only a very tiny bit' or 'barely noticeably'.
Das neue Modell ist nur minimal teurer als das alte.
The new model is only minimally more expensive than the old one.
In the meaning of 'very small', 'minimal' is often combined with nouns that describe an amount, a degree, or a change. Typical examples are 'ein minimaler Aufwand' (minimal effort), 'minimale Kosten' (minimal costs), or 'eine minimale Verbesserung' (a minimal improvement).
Für die Reparatur ist nur ein minimaler Aufwand nötig.
Only minimal effort is needed for the repair.
When 'minimal' is used in connection with art, architecture, or design, it describes a style that focuses on the essentials. Here it does not just mean 'very small', but 'deliberately reduced'.
Der Architekt ist bekannt für sein minimales Design.
The architect is known for his minimal design.
at least
'mindestens' and 'minimal' both have to do with a lower or very small amount. Even so, they are used differently. 'mindestens' is an adverb and gives a limit: it should not be less. 'minimal' is an adjective and describes something as very small or as the smallest possible. They can be confused because both make you think of a minimum. 'mindestens' is more natural with requirements such as time, money, or number. 'minimal' fits when you are describing size, effort, or a difference.

Der Unterschied zwischen den beiden Preisen ist minimal.
The difference between the two prices is minimal.
Bei der Arbeit habe ich aus Zeitmangel mindestens drei Aufgaben verschoben.
At work, I postponed at least three tasks because I didn't have enough time.