If A, B, C are the sets of all positive divisors of  ${10}^{30},{20}^{20}and{30}^{10}$respectively. Then n$(A\cup B\cup C)$  equals 

Given $A$ is the set of all positive divisors of ${10}^{30}=2^{30}·5^{30}$

Hence, $n\left(A\right)=31·31$

Given $B$ is the set of all positive divisors of ${20}^{20}=2^{40}·5^{20}$

Hence, $n\left(B\right)=41·21$

Similarly, $n\left(C\right)=11·11·11$

Consider, $n\left(A\cap B\right)$ . It is the set of all divisors of ${10}^{30},{20}^{20}$

This is the number of divisors of $2^{30}{5}^{20}$

So that $n\left(A\cap B\right)=31·21$

Similarly, $n\left(B\cap C\right)=11·11$ and $n\left(A\cap C\right)=11·11$

$n\left(A\cap B\cap C\right)=11·11$

Use the formula for the cardinal number of sets ,we get $n\left(A\cup B\cup C\right)=2381$