The Church has long maintained, as attested to be references in the writings of General Authorities, that the Hill Cumorah in western New York state is the same as referenced in the Book of Mormon.
F. Michael Watson - First Presidency Secretary
Letter dated October 16, 1990
It is known that the Hill Cumorah where the Nephites were destroyed is the hill where the Jaredites were also destroyed. This hill was known to the Jaredites as Rama…
**The Prophet Joseph Smith himself is on record, definitely declaring the present hill called Cumorah to be the exact hill spoken of in the Book of Mormon. **
Further, the fact that all of his associates from the beginning down have spoken of it as the identical hill where Mormon and Moroni hid the records, must carry some weight. It is difficult for a reasonable person to believe that such men as Oliver Cowdery, Brigham Young, Parley P. Pratt, Orson Pratt, David Whitmer, and many others, could speak frequently of the Spot where the Prophet Joseph Smith obtained the plates as the Hill Cumorah, and not be corrected by the Prophet, if that were not the fact. That they did speak of this hill in the days of the Prophet in this definite manner is an established record of history…"
Joseph Fielding Smith - Mormon prophet
Doctrines of Salvation, Vol.3, p.232-43.
n the western part of the state of New York near Palmyra is a prominent hill known as the “hill Cumorah.” (Morm. 6:6.) On July twenty-fifth of this year, as I stood on the crest of that hill admiring with awe the breathtaking panorama which stretched out before me on every hand, my mind reverted to the events which occurred in that vicinity some twenty-five centuries ago—events which brought to an end the great Jaredite nation…
This second civilization to which I refer, the Nephites, flourished in America between 600 B.C. and A.D. 400. Their civilization came to an end for the same reason, at the same place, and in the same manner as did the Jaredites’.
Marion G. Romney - First Presidency Counselor
Ensign, November 1975, p.35
Both the Nephite and Jaredite civilizations fought their final great wars of extinction at and near the Hill Cumorah (or Ramah as the Jaredites termed it), which hill is located between Palmyra and Manchester in the western part of the State of New York.
Joseph Smith, Oliver Cowdery and many of the early brethren, who were familiar with all the circumstances attending the coming forth of the Book of Mormon in this dispensation, have left us a pointed testimony as to the identity and location of Cumorah or Ramah.
Bruce R. McConkie - Mormon apostle
Mormon Doctrine, p. 174-175
This time it will have to do with so important a matter as a war of extinction of two peoples, the Nephites and the Jaredites, on the self same battle site, with the same ‘hill’ marking the axis of military movements. By the Nephites this ‘hill’ was called the ‘Hill Cumorah,’ by the Jaredites the ‘Hill Ramah’; it was that same ‘hill,’ in which the Nephite records were deposited by Mormon and Moroni, and from which Joseph Smith obtained the Book of Mormon, therefore the ‘Mormon Hill,’ of today—since the coming forth of the Book of Mormon—near Palmyra, New York.
B.H. Roberts - Mormon apostle and LDS church historian
Studies of the Book of Mormon, p.277