Let $\mathrm{AP}(\mathrm{a} ; \mathrm{d})$ denote the set of all the terms of an infinite arithmetic progression with first terma and common difference $\mathrm{d}>0$. If $\operatorname{AP}(1 ; 3) \cap \operatorname{AP}(2 ; 5) \cap \operatorname{AP}(3 ; 7)=\operatorname{AP}(\mathrm{a} ; \mathrm{d})$ then $\mathrm{a}+\mathrm{d}$ equals $\_\_\_\_$