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-(이)라도 (-irado) is a particle which can be translated as "at least," or "even if it's just...." It is attached to the end of nouns. The noun that this particle -라도 (-rado) is attached to is what is "at least." A verb is not necessary, but a complete sentence usually conveys a full complete idea, whereas having (noun)라도 would require some inference from the listener.

The words 저거도 (jeogeodo) and 최소한 (choesohan) also mean "at least" as well, but they are used as noun modifiers. (이)라도 is used as a particle.

Formation
(명사) + (이)라도
(Noun) + (i)rado

-라도 (-rado) is used with nouns that end in vowels.
쥬스 (juseu) - Juice
쥬스 + 라도
쥬스라도 (juseu-rado) - At least juice

-이라도 (-irado) is used with nouns that end in consonants.
물 (mul) - water
물 + 이라도
물이라도 - at least water

Example Sentences
1. 전화번호라도 주세요.
Please give me at least your phone number.

2. 명함이라도 주세요.
Please give me at least your business card.