go to the state where your great grandmother lived and search for her marriage record under her first husband
name, once you obtain the marriage certificate, both her first husbands name will be on it and your greatgrandmother name will be on it.
you can first start by google the state where they were married and see if their name and certificate number etc is on line, remember you can look for the marriage certificate under her first husbands name, since you do not know her maiden name. Thus you will apply for the certificate under his name.