For two cultures that are found on opposite sides of the planet, there are a disproportionate number of similarities in the laws, customs and traditions of the two groups. One would normally expect to see a greater amount of difference in religious beliefs such as is found in other cultures that demonstrate animal worship, nature worship, ancestor worship, multiplicity of gods, such as in found amongst the Greeks, Romans, Egyptians, Vikings, Chinese, etc, etc. This essay will go through a number of these "evidences":
First Claim of the Book of Mormon
One of the very first claims of the Book of Mormon, (made in its own Title Page and first published in 1829) is that the people in the Americas are part of the Lost Ten Tribes, "a remnant of the House of Israel".
Even though the history recorded therein tells the story of a great people who lost their way, rejected their God and suffered divine punishments accordingly, it would be quite natural to expect that their descendants, some 1500 years later, would still retain some significant traces, signs, traditions, laws and customs of their Judaic heritage.
Another major note is that the ancient Mormon prophets repeatedly wrote that this particular record was a condensed historical version of their significant religious experiences. One would have to assume that their record would be limited to those events taking place in their own communities and that over many centuries their peoples would branch off into many communities spread out across a very great continent and it would be impossible for them to know what took place in every part of the continent.
Prophecies of Gathering Israel
27 And the Lord shall scatter you among the nations, and ye shall be left few in number among the heathen, whither the Lord shall lead you. (Moses in Deuteronomy 28:64)
There are multiple prophecies in the Bible that the twelve tribes of Israel will be scattered and then gathered from the four corners of the Earth. This prophesy is echoed by the Book of Mormon with emphasis that it includes the American continent. So strong are these prophecies that they constitute one of the Thirteen Articles of Faith of the church. Therefore you can ask: "What evidences are there that any of the lost tribes of Israel ever lived in America? The evidences are many as will be shown below.
In the Old Testament of the Bible, the great righteous patriarch Abraham was promised a numerous posterity  and through his seed all the earl would be blessed.  This covenant was renewed with his son Isaac  and his grandson Jacob/Israel.. Ancient prophets, including Moses, foretold that Israel would be scattered.  The Northern tribes were then carried from Jerusalem to Babylon between 605 BC and 597 BC (see 2 Chronicles 36).
Do you believe the many Biblical prophecies that scattered Israel will be gathered in the last days from the four corners of the earth? These prophecies are found in Jeremiah 23:3, Jeremiah 30:3,8, [Deuteronomy 4:23-32, Isaiah 43:1-6 and elsewhere.
When getting ready to cross the River Jordan to possess the promised land, Moses had the people of Israel swear to covenant to the effect if they sinned they would be sorely cursed and scattered, but there was still the promise that in the last days the Lord would gather their repentant descendants "That then the Lord thy God will turn thy captivity, and have compassion upon thee, and will return and gather thee from all the nations, whither the Lord thy God hath scattered thee. If any of thine be driven out unto the outmost parts of heaven, from thence will the Lord thy God gather thee, and from thence will he fetch thee: (Deut 30:3-4 (See Ch 29:10 to 30:10))
"And it shall come to pass in that day, that the Lord shall set his hand again the second time to recover the remnant of his people, which shall be left, from Assyria, and from Egypt, and from Pathros, and from Cush, and from Elam, and from Shinar, and from Hamath, and from the islands of the sea. And he shall set up an ensign for the nations, and shall assemble the outcasts of Israel, and gather together the dispersed of Judah from the four corners of the earth. (Isaiah 11.11-12)
See Also :
- New Era 2019 - Prophesied thousands of years ago, it’s the greatest work on earth today!
- Lesson 23
- Old Testament Prophecies
"10 We believe in the literal gathering of Israel and in the restoration of the Ten Tribes; that Zion (the New Jerusalem) will be built upon the American continent; that Christ will reign personally upon the earth; and, that the earth will be renewed and receive its paradisiacal gglory. (LDS Church 10th Article of Faith)
Earlier Scientific Research
But the Book of Mormon is not the first published work to make this bold claim! Their were many other earlier American writers to make similar claims and presented those claims with their authoritative research. Many of these were published long before Joseph Smith was born. Others were published well after his death. Here are some of the more notable works.
James Adair History (1775)
This book, published 55 years beforehand, contains some powerful evidences for why Mr. Adair strongly felt from his forty years of personal observations that the American Indians were direct descendants of The House of Israel, and perhaps part of the Lost Ten Tribes. In his efforts to scientifically determine their historical origins, the first 100 pages of his book presents 23 "Arguments" or essays supporting this claim.
- Citations from Native American Historians
A Star in the West A Humble Attempt to Discover the Long Lost Ten Tribes of Israel; Preparatory to Their Return to Their Beloved City, Jerusalem by Elias Boudinot: A Star in the West is an investigation by Elias Boudinot into the widely-held belief that the Native Americans were descended from the lost tribes of Israel.
At the time he published his book, this famous American statesman, Elias Boudinot, was President and Co-Founder of the American Bible Society. In his book, Mr. Boudinot presents a number of essays for why the Native Americans were descendants of ancient Hebrews. He includes many citations from the Book of Isaiah. (See Also Biblical References to the Book of Mormon.)
This Bible Society President was particularly concerned with the discovery of the Lost 10 Tribes:
"But as to the majority of the ten tribes, although every believer in divine revelation has no doubt of their being preserved by the sovereign power of God in some unknown region; yet as the whole globe has been traversed by one adventurer or another, it is a little astonishing that they have not hitherto been discovered. By the representation above, it is clear that we must look for them, and they will undoubtedly, at last be found, in the western regions, or some place answering this description as the place of their banishment. 
Judaic Tribal Organization
They are strongly affiliated in family clans resembling that of House of Israel in the old testament.
- While strongly hostile and distrusting to other clans, they are fiercely loyal to their own clan.
- Amongst their own clan they will freely share "all things in common" - reminscent of 4th Nephi in the Book of Mormon and The United Order
- Tales of all tribes originally crossing the Mississippi River from the western territories centuries ago.
- Similarities in tribal languages, while different they had strong similarities in structure. For example they all had the same term for buffalo, "Yanasa".
(To be researched) Both the Cherokee and Jews count your primary heritage from your mother's side.
- Note: Luke's tradition of the Ancestry of Jesus from his mother's side.
- Boudinot : Pg 26. - intro summary. Study history of Israel.
- Boudinot uses the histories of Colden, Adair, Brainerd, Edwards, Beatty and Bartrum.
- And follows the apocryphal account of Esdras about the lost of ten tribes.
- Historicity of the Book of Mormon
- Isaiah 43:1-6. Gather children from afar.
- Isaiah 49:8-13
- Ezekiel 37:16 write on the stick for Israel “and her companions”
- Zach. 8:7-8 great celebration when come.
- Ezekiel 20:35-43. Lord pleads with lost tribes to return to his kingdom in the last days.
- Ezekiel has Many references to Judah in the "East" and Ephraim in the "West" countries.