Question 251658
let the 3 consecutive odd no.s be 2t-1, 2t+1, 2t+3

so n= {{{1+(2t-1)^2+(2t+1)^2+(2t+3)^2}}}

expanding the terms and simplifying we get 

n={{{12(t^2+t+1)}}}

so the largest common factor of all such no.s n is 12.

ans: 12