The period of sin πx12+cos πx4+tanπx3,Where x represents the greatest integer less than or equal x is

Since, sinπx+2412=sinπ1224+x                         =sin2π+πx2=sinπx12The period of sin πx12 is 24.Similarly, period of cos πx4 is 8 and period of tanπx3=3.Hence, the period of the given function =LCM of 24,8,3=24.