We want to find a number divisible by all the integers from 1 to 10 and we want to find the smallest of such numbers.The least number divisible by all the integers from \\\\(1\\\\) to \\\\(10\\\\) will be the L.C.M of \\\\(1, 2, 3, 4, 5, 6, 7, 8, 9, 10\\\\). Writing out the numbers as a product of prime factors, we get -\\\\(1=1\\\\)\\\\( 2=2\ imes 1\\\\)\\\\( 3=3\ imes 1\\\\)\\\\( 4=2\ imes 2\\\\)\\\\( 5=5\ imes 1\\\\)\\\\( 6=2\ imes 3\\\\)\\\\( 7=7\ imes 1\\\\)\\\\( 8=2\ imes 2\ imes 2\\\\)\\\\( 9=3\ imes 3\\\\)\\\\(10=2\ imes 5\\\\)So, the L.C.M. of these integers is \\\\(1\ imes 2\ imes 2\ imes 2\ imes 3\ imes 3\ imes 5\ imes 7=2520\\\\)Hence, the least number divisible by all the numbers from \\\\(1\\\\) to \\\\(10\\\\) is \\\\(2520\\\\)