It's difficult! But can you solve it?

$factorize\quad \\ ({ p }^{ 2 }-1)({ q }^{ 2 }-1)({ r }^{ 2 }-1)\\ we\quad know\quad that\quad all\quad prime\quad number\quad can\quad be\quad write\quad as\quad 6k\pm 1\\ .\\ let,\\ p=6k\pm 1\\ q=6m\pm 1\\ r=6n\pm 1\\ .\\ so,\quad that\quad it\quad can\quad be\quad written\\ { 12 }^{ 3 }kmn(3k\pm 1)(3m\pm 1)(3n\pm 1)\\ .\\ k=m=n=1\quad is\quad the\quad smallest\quad value.\\ so,\quad the\quad greatest\quad divider\quad is\quad { 12 }^{ 3 }{ 2 }^{ 3 }=13824\\ \\$