"I have not... [noun phrase]" is outdated in English. It is very old. Today, we say, "I do not (or: don't) have...[noun phrase]". Therefore: "I don't have a pen." "I don't have the least idea" might be grammatically correct, but it does not sound natural. It is more common to say "I don't have any idea" or "I don't have the slightest idea" or "I don't have the foggiest idea." You can also say: "I haven't got the slightest/least idea."

It would be "I have the least idea" Which just means 'I do not know'. --------- Another example would be "She hasn't the least interest", which just means 'She has no interest'.