Whenever the number of candidates for any office requires the use of more than one row or column on a voting machine or whenever the official or agency having the responsibility to determine ballot positions determines that the number of candidates for an office requires the use of more than one column on a ballot, the official or agency having such responsibility shall require that the rows or columns be rotated in such a manner that all rows are positioned on top, or all columns are positioned to the left, in an equal number of wards or election districts. If the number of wards and election districts in which voting for an office is conducted is not equally divisible, the position of the rows or columns in the remaining wards or election districts shall be determined by the official or agency by the drawing of lots. The number of columns or rows shall be determined at the same time that the positions of the candidates’ names are determined for each primary and election.