Let's try it this way: He came to me and asked for money-two consecutive actions--first he came then asked He came to me to ask for money-- he came on purpose to ask for money or came in order to ask for money.
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New2grammarHe came to me [to ask/and asked] for money.
Which one is more commonly used?
IMO, both are commonly used.
I would write the sentence as follows:
He came to ask me for money.