If $$P_1$$, $$P_2$$, and $$P_3$$ are three distinct prime numbers, then what is the least common multiple of $$P_1$$, $$P_2$$, and $$P_3$$?

$$ {1\over {^3\sqrt{4}+{^3\sqrt{2}}}+1}=a^3\sqrt{4}+ b^3\sqrt{2}+c $$ and a, b, c are rational numbers, then a + b + c is equal to

If a = 2·361, b = 3·263 and c = 5·624, then the value of a³ + b³ – c³ + 3abc is

If p, q, r are all real numbers, then (p – q)³ + (q – r)³ + (r – p)³ is equal to 

If x = 2 - 2^1/3 + 2^2/3, then the value of x³– 6x² + 18x + 18 is

If x = – 1, then the value of   $$ {1\over x^{99}}+{1\over x^{98}}+{1\over x^{97}}+{1\over x^{96}}+{1\over x^{95}}+{1\over x^{94}}+x $$ is

$$x+{1\over x}=2$$ and x is real, then the value of $$x^{17}+{1\over x^{19}}$$ is

If x = 19 and y = 18, then the value of   $$ {{x^2}+{y^2}+{xy}}\over x^3-y3 $$ is