The number x is divisible by 7, ⇒ x=7k Now L.C.M. (8,12,16) = 48 Thus, the least number which is divided by 8, 12 and 16 and leaves a remainder 3 in each case = 48n+3 Now, f(n)=(48n+3) should be divisible by 7. By putting n=1,2,3,... f(1)=48(1)+3=51 f(2)=48(2)+3=99 f(3)=48(1)+3=147 which is divisible by 7.