Given that $:2^{\frac{1}{3}},3^{\frac{1}{4}},4^{\frac{1}{6}},6^{\frac{1}{8}},10^{\frac{1}{12}}$
LCM of $3,4,6,8,12 = 24$
Now, $2^{\frac{1}{3}\times 24},3^{\frac{1}{4}\times24},4^{\frac{1}{6}\times24},6^{\frac{1}{8}\times24},10^{\frac{1}{12}\times24}$
$\implies2^{8},3^{6},4^{4},6^{3},10^{2}$
$\implies 256,729,256,216,100$
$\therefore$ The largest number is $ = 729$
So, the correct answer is $(B).$