The minimum age of a presidential candidates must be:

Age of candidacy is the minimum age at which a person can legally qualify to hold certain elected government offices. In many cases, it also determines the age at which a person may be eligible to stand for an election or be granted ballot access.

The first known example of a law enforcing age of candidacy was the Lex Villia Annalis, a Roman law enacted in 180 BCE which set the minimum ages for senatorial magistrates.

the fifth and fourteenth amendments to the united states constitution each contain a due process clause. due process deals with the administration of justice and thus the due process clause acts as a safeguard from arbitrary denial of life, liberty, or property by the government outside the sanction of law.

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