1. Let $a$ and $b$ be positive integers, $1176a=b^{4}$. Find the minimum value of $a$.

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(Note: Observing that $b^{4}=1176 a=2^{3} \times 3 \times$ $7^{2} a$, then $a$ must contain the factor $2 \times 3^{3} \times 7^{2}$. Thus, the minimum value of $a$ is $2 \times 3^{3} \times 7^{2}=2646$.)