Mínimo

English is full of synonymous pairs of words, one from a Romance language and one from a Germanic language. A good example is minimum from Latin and least from Old English. When the Normans conquered England, French vocabulary began to be used in government and administration without supplanting the Anglo-Saxon vernacular used in daily life. As a result, English words of Romance origin tend to be formal in nature when compared to their Anglo-Saxon counterparts.

Lo mínimo

This explains why minimum belongs to a more formal style in English than in Spanish. Between friends, in English we usually say It's the least (not 'minimum') I can do (for you), but in Spanish it would be Es lo mínimo que puedo hacer (por ti). The take-away point here is to remember that words that feel formal to you in Spanish may, in reality, belong to a neutral style.

So keep in mind that mínimo a perfectly neutral word in Spanish. As you can see below, its best translation often involves least, not minimum or minimal.

At least

When set apart from the rest of the utterance, mínimo commonly means the least (you could do). It often carries a touch of impatience, exasperation or pleading.

• Mínimo dale chance. Give him a chance. That's not much to ask. Do at least that much.
• Mínimo me puedes ... Ok. But at least you could ... for me. At a bare minimum, ....
• Mínimo debes ir dos veces por semana. You should go at least twice a week. The least you should go is twice a week. The mínimo can go at the end as well: Debes ir dos veces por semana, mínimo.

Although at least works for mínimo in these examples, a different meaning of at least, a resignation of sorts, would require al menos: Al menos me quiere. At least he loves me.

En lo más mínimo

En lo más mínimo means not at all, not even a bit: No me suena en lo más mínimo. No me suena para nada. That doesn't ring a bell at all.