The quotient of 3 times a number and 16 is 12. Find the number

64

Step-by-step explanation:

3n÷16=12

3n=12×16

3n=192

3n/3=192/3

n=64

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18