if m is the smallest positive integer such that m! is a multiple of 4125, and n is the smallest positive integer such that n! is a multiple of 2816000, then find n-m.
+150 \(4125=3\times 5^3\times 11\) first 3 multiple of 5 : 5,10,15
m = 15
\(2816000=2^{11}\times 5^3\times 11\) multiple of 2 : \(2, 2^2, 2\times 3, 2^3, 2\times 5, 2^2\times 3, 2\times 7\)
n=15
n - m = 15 - 15 = 0
