Determine the largest possible value of B such that it is a multiple of all positive whole numbers less than ³√B.
Consider x,x-1,x-2,x-3
If x is a multiple of 3, then LCM of these = x*(x-1)*(x-2)*(x-3)/6
Otherwise, LCM = x*(x-1)*(x-2)*(x-3)/2
This should be less than (x+1)³.
Case1: x≤12
Case2: x<8
x can take values {1,2,3,4,5,6,7,9,12}
But checking for x=9,12 gives no solution.
For x=7, LCM=420<8³.
Largest Possible Value of B=420.
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Posted by Praneeth
on 2007-08-14 06:46:51 |
Solution
