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Value of n

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Value of n

by Baten80 » Fri Sep 24, 2010 10:34 am
n is a positive integer, and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1440, then the smallest possible value of n is

A. 8
B. 12
C. 16
D. 18
E. 24
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by clock60 » Fri Sep 24, 2010 10:47 am
here i got A
if n=8, then k=1*2*3*4*5*6*7*8. and this number must be multiple of 1440=2^5*3^2*5
k must have at least 2^5 and it has (2*2^2*2 (from 6)*2^3 (from 8). at least 3^2 ( 3*3 (from 6), at least one 5 also has
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