The positive integers that are <= 10 and are coprime to 10 are 1,3,7,9; lcm(1,3,7,9) = 63. Now the positive integers that are coprime to 10 form a sequence that begins: 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49, 51, 53, 57, 59, 61, 63, 67, 69, ...

Since 63 is the 26th of these integers, a(10) = 26.