Aspire Faculty ID #16589 · Topic: NIMCET 2008 · Just now
NIMCET 2008

If both $7^2$ and $3^3$ are factors of $a\times11^3\times6^2\times13^{11}$, then the smallest possible value of $a$ is

Solution

$6^2=(2^2)(3^2)$ gives only $3^2$. To make $3^3$, one more $3$ is needed, and $7^2$ is missing completely. So $a=3\times7^2=147$.

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