spätestens
at the latest
Indicates the latest possible point in time; no later than the stated time or deadline.
Die Bewerbung muss spätestens am Freitag bei uns eingehen.
The application must reach us by Friday at the latest.

at the latest
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at the latest
Indicates the latest possible point in time; no later than the stated time or deadline.
Die Bewerbung muss spätestens am Freitag bei uns eingehen.
The application must reach us by Friday at the latest.

'Spätestens' (at the latest) is a form of the superlative of 'spät' (late). The ending '-ens' forms an adverb that indicates an outer limit or the latest possible point in time.
Ich rufe dich spätestens heute Abend zurück.
I’ll call you back by this evening at the latest.
'Spätestens' (at the latest) usually stands directly before the time expression it limits. If it stands at the beginning of the sentence for more emphasis, the verb follows directly after it in position 2.
Du musst den Antrag spätestens bis Montag abgeben.
You have to submit the application by Monday at the latest.
Common combinations are points in time with 'um' (spätestens um 15 Uhr — at 3 p.m. at the latest), days with 'am' (spätestens am Mittwoch — by Wednesday at the latest), or deadlines with 'bis' (spätestens bis Ende der Woche — by the end of the week at the latest).
Wir sollten spätestens um 10 Uhr losfahren, um den Zug nicht zu verpassen.
We should leave by 10 o’clock at the latest so we don’t miss the train.
maximum
'spätestens' and 'maximal' both state a limit. The important difference is: 'spätestens' refers to time and means that something must not happen after a certain point in time. 'maximal' states an upper limit for quantity, size, duration, or intensity. Learners may confuse the words because both express a kind of endpoint or limit. In practice: for deadlines and times, 'spätestens' usually fits; for numbers, amounts, and measurements, 'maximal' usually fits.

Im Urlaub schreibe ich dir spätestens am Sonntag eine Nachricht.
While I'm on vacation, I'll send you a message by Sunday at the latest.
In der kleinen Werkstatt dürfen maximal drei Personen gleichzeitig arbeiten.
In the small workshop, a maximum of three people may work at the same time.