Both of the previous marriages of either a Prime Minister or an ordinary Catholic, would need to be found invalid by the Catholic Church.
The validity of marriage is determined by the following factors
- Freedom to marry
- Open to life
Can. 1055 §1. The matrimonial covenant, by which a man and a woman establish between themselves a partnership of the whole of life and which is ordered by its nature to the good of the spouses and the procreation and education of offspring, has been raised by Christ the Lord to the dignity of a sacrament between the baptized.
Can. 1057 §1. The consent of the parties, legitimately manifested between persons quali-fied by law, makes marriage; no human power is able to supply this consent.
There must not be any impediments. Examples are inability to consent, a dispensation not being given, or the couple being too closely related.
The simplest scenario is a baptized Catholic who married outside of the Church without a dispensation. Catholics are required to follow canonical form when getting married and a marriage without a dispensation is not valid . If someone were to do this twice, and then revert to the faith, or wish to marry a practicing Catholic, they would very likely be able to get declarations of nullity for their previous marriages easily.
Note: They would have had to be received into the Catholic Church prior to the marriage they are seeking a decree of nullity for
Can. 1108 §1. Only those marriages are valid which are contracted before the local ordinary, pastor, or a priest or deacon delegated by either of them, who assist, and before two witnesses according to the rules expressed in the following canons and without prejudice to the exceptions mentioned in cann. 144, 1112, §1, 1116, and 1127, §§1-2.
Also, less likely, but if their previous spouses died after the divorces the surviving spouse would be free to marry.
Code of Canon Law - marriage
Code of Canon Law - impediments
Code of Canon Law - anullments