The correct answer to this open question is the following.
Historians think that it took approximately two centuries from the time Islam was introduced until it became the religion of the majority population in Egypt, Syria, Iran, and Spain.
In the always interesting history of the spread of Islam through different regions, the caliphates were the new form of government after the death of Muhammad. Then, many missions to teach the religious principles of Islam were launched over many places and this factor, as well as trade, allow the expansion of Islam from the Arab peninsula until far places such as the Middle East, North Africa, and the Iberian peninsula.