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# If x and y are consecutive positive iteger multiple of 3,

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Manager
Joined: 18 Aug 2005
Posts: 85
Location: Italy, Rome caput mundi
Followers: 1

Kudos [?]: 12 [0], given: 0

If x and y are consecutive positive iteger multiple of 3, [#permalink]  07 Sep 2005, 04:24
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If x and y are consecutive positive iteger multiple of 3, what is the greatest integer J such that XY/J is always an iteger?
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VP
Joined: 13 Jun 2004
Posts: 1122
Location: London, UK
Schools: Tuck'08
Followers: 7

Kudos [?]: 31 [0], given: 0

I agree, smallest number is 18 (3*6).
Then after those 2 first numbers all 2 consecutive multiples of 3 will be formed by :
- a multiple of 3 (odd)
- a multiple of 2 and 3 so always a mutliple of 6 (even)

so definitely divisible by 18
Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 181 [0], given: 2

18 for me and this is how I would do it...

so we have x=3m
and y=3n

y*x=9 m*n

so J has to be J= A*9 M*N

so lets look at multiples of 3, say 3 and 6

prime factors are 3, 3, 2, so we got 3^2*9 as the largest factor for which all consecutive multiples of 3 will be divisible by...

18 it is..
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