The Laycock family came to Utah between 1861 and 1863. Their PEF loan was recorded in 1863 (an indication that they possibly traveled to Utah in 1863), but they both stated that they came to America in 1861 in the 1880 and 1900 U.S. censuses. But the first documentation to place them in Utah is Archibald's rebaptism in American Fork on 14 August 1864 which was prior to the arrival of that season's emigration. Further research is needed to narrow the year of their travel.
Birth and death date is confirmed by Find A Grave website.