<s>[INST] Determining the smallest possible value If both $11^2$ and $3^3$ are factors of the number $a \times 4^3 \times 6^2 \times 13^{11}$, then what is the smallest possible value of a?

IS there any trick to answer this type question quickly?

 [/INST] HINT:
As $(4,11)=(6,11)=(13,11)=1$
$11^2$ must divide  $a$
Observe that the highest power of $3$ in $4^3 \times 6^2 \times 13^{11}$ is $2$
So, $3$ must divide $a$
$\implies $lcm$(11^2,3)$ must divide $a$
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