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If n is a positive integer and the product of all integers

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If n is a positive integer and the product of all integers [#permalink]

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New post 07 Nov 2009, 11:02
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If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?
A. 10
B. 11
C. 12
D. 13
E. 14
[Reveal] Spoiler: OA

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Expert Post
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Kudos [?]: 70541 [0], given: 9849

Re: If n is a positive number Gmat prep [#permalink]

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New post 07 Nov 2009, 13:18
Expert's post
If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?
A. 10
B. 11
C. 12
D. 13
E. 14

\(990=2*5*3^2*11\)

We are told that \(n!=990*k=2*5*3^2*11*k\) which means that n! must have all factors of 990 to be the multiple of 990, hence must have 11 too, so the least value of n is 11 (notice that 11! will have all other factors of 990 as well, otherwise the least value of n would have been larger).

Answer: B.
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If n is a positive [#permalink]

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New post 12 Dec 2011, 06:47
If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?

Guys - any idea how to solve this questions? OA is not provided unfortunately.
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Re: Multiple of 990 [#permalink]

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New post 12 Dec 2011, 07:55
is it 11 ?
990 = 2 * 5 * 9 * 11
so the least value for "N" can be 11.
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Re: Multiple of 990 [#permalink]

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New post 12 Dec 2011, 23:12
990= 11*10*9


since 11 is a prime no which does not have factor apart from 11 and 1. so 11 is necessary no for 990.

hence n=11
Re: Multiple of 990   [#permalink] 12 Dec 2011, 23:12
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