No, the sides of a triangle cannot have lengths of 1, 2, and 3 because the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, 1 + 2 = 3, which means that the side with length 3 is not greater than the other two sides. Therefore, a triangle cannot be formed with sides of length 1, 2, and 3.