Which of the following amendments granted women the right to vote?

The 19th Amendment, ratified in 1920, explicitly prohibits the federal and state governments from denying the right to vote on the basis of sex, thus granting women the right to vote in the United States. This amendment was the culmination of a long and arduous struggle by women's suffrage activists who campaigned for decades to obtain equal voting rights.

The 15th Amendment, ratified in 1870, addressed voting rights but focused on prohibiting the denial of the right to vote based on race, color, or previous condition of servitude, without mentioning gender. The 24th Amendment, ratified in 1964, prohibits poll taxes in federal elections but does not pertain to gender or women’s voting rights specifically. The 1st Amendment protects freedoms concerning religion, expression, assembly, and the right to petition, but again, does not relate to voting rights.

Thus, the correct answer is the 19th Amendment, as it directly addresses and guarantees women's right to vote in the United States.