(Q). Find the smallest perfect square number divisible by 11!.
Solution:-
11! = 11×10×9×8×7×6×5×4×3×2×1
= 11×2×5×3²×2³×7×2×3×5×2×2×3×2
= 11×7×5²×3⁴×2⁸
Hence smallest perfect square number will be
=11²×7²×5²×(3²)²×(2⁴)²
= 11!×11×7
= 307359300 Answer