ABC26GN1419 · Square Roots and Cube Roots

$$\begin{aligned} 7! & =7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \\ & =7 \times 2 \times 3 \times 5 \times 2^{2} \times 3 \times 2 \\ & =2^{4} \times 3^{2} \times 5 \times 7 \end{aligned}$$ Thus, the smallest perfect square number which is divisible by $7!$ is $$\begin{aligned} \left(2^{4} \times 3^{2} \times 5 \times 7\right) & \times(5 \times 7) \\ =5040 & \times 35=176400 . \end{aligned}$$