If

$15 \times 14 \times 13 \times \dots \times 3 \times 2 \times 1 = 3^m \times n$

where $m$ and $n$ are positive integers, then what is the maximum value of $m$ ?

Kepler. Discussing PYQs. Q.no. 74

If 15×14×13×⋯×3×2×1=3m×n15 \times 14 \times 13 \times \dots \times 3 \times 2 \times 1 = 3^m \times n15×14×13×⋯×3×2×1=3m×n where mmm and nnn are positive integers, then what is the maximum value of mmm ?