How to Say "greatest possible" in Spanish
The Spanish word for “greatest possible” is “máxima” — A2 level. This is a very common word in everyday Spanish.
English → SpanishA2
AdjectiveA2
as in capacity or importance

Examples
La velocidad máxima permitida en esta carretera es 100 km/h.
The maximum speed allowed on this road is 100 km/h.
Necesitamos la máxima atención para resolver este problema.
We need the greatest possible attention to solve this problem.
El equipo mostró una calidad máxima en la final.
The team showed top quality in the final.
Gender Agreement
Remember that 'máxima' is the feminine form. You must use it when describing feminine nouns (e.g., la velocidad máxima). For masculine nouns, use 'máximo' (e.g., el esfuerzo máximo).
Related Translations
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