## EXPERT ANSWER

Let gcd(a,b,c) = m.Therefore, m divides a, b and c.Then, gcd(a,b) = mx, gcd(b,c) = my, gcd(a,c) = mz where x, y, z are all greater than or equal to 1.

Thus, gcd(a,b)xgcd(b,c)x gcd(a,c) = mxmymz = xyzm^{3}

And [gcd(a,b,c)]^{3} = m^{3}.

xyzm^{3} is greater than or equal to m^{3}

Therefore, gcd(a,b)xgcd(b,c)x gcd(a,c) is greater than or equal to gcd(a,b,c).

If a/m, b/m, c/m are pairwise coprime, then x=y=z=1.And hence in this case, gcd(a,b)xgcd(b,c)x gcd(a,c) = gcd(a,b,c).