But $n = 15$: $15 \cdot 17 \cdot 19 \cdot 21 = 3 \cdot 5 \cdot 17 \cdot 3 \cdot 7 \cdot 3 \cdot 7 = 3^3 \cdot 5 \cdot 7^2 \cdot 17$ — divisible by $27$.