The smallest positive integer that does not divide 1 × 2 × 3 × 4 ×...

Let $n$ be a smallest integer that does not divide $1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9$ Prime factorisation $=2^7 \times 3^4 \times 5 \times 7$ Clearly we can see that 2 and 7 factor of 2 will divide 9 ! Also 3 and 4 factors of 3 will divide 9 ! So number i.e. $2,3,2^2, 5.2 .3,7,2^3, 3^3, 5.2$, will divide 9 ! Therefore, least positive integer that does not divide 9 ! is 11