It is Monday, and I want to tell my colleague I was not in the office the week before (last week?).
Would it be ok to say:
I took last week off
Is that correct?
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Both of these work in your context:
I took last week off.
I took the last week off.
The difference in meaning is very slight, and is irrelevant in your current case, because it's Monday. But on different days, the meaning is different.
Imagine that you sent this on Wednesday instead of Monday. Now the meanings are different. "I took last week off" implies that you were not at work from two Mondays ago until the previous Friday. "I took the last week off" implies that you were not at work from the previous Wednesday through yesterday (Tuesday).
I don't know why, but the "the" allows the time period to be misaligned to the week boundary.