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# If n and t are positive integers, what is the greatest prime

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Manager
Joined: 25 Aug 2007
Posts: 63
Schools: HBS '10
If n and t are positive integers, what is the greatest prime  [#permalink]

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18 Oct 2007, 21:15
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If n and t are positive integers, what is the greatest prime factor of the product nt?

(1) The greatest common factor of n and t is 5
(2) The least common multiple of n and t is 105

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Director
Joined: 03 May 2007
Posts: 769
Schools: University of Chicago, Wharton School
Re: GMATprep DS - prime factors  [#permalink]

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18 Oct 2007, 21:45
1
Big-O wrote:
If n and t are positive integers, what is the greatest prime factor of the product nt?

(1) The greatest common factor of n and t is 5
(2) The least common multiple of n and t is 105

B.

1: Could be n and t could be either 55 or 65.
2: LCM = 105 means 7 is the gratest prime factor.
VP
Joined: 08 Jun 2005
Posts: 1098

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19 Oct 2007, 03:23
2
GCF - Greatest Common Factor

Largest possible common factor between numbers

LCM - Lowest Common Multiple

Largest possible common multiple between numbers

To find the GCF/LCM, you will need to do prime-factorization. This means reducing a number to its prime-factor form.

E.g. 1

GCF/LCM of 4,18

4 = 2*2
18= 2*3*3

To find the GCF, take the multiplication of the common factors (pick the lowest power of the common factors) In this case, GCF = 2.

To find the LCM, take the multiplication of all the factors (pick the higest power of the common factors). In this case, LCM=2*2*3*3=36

------------------------------------------------------------------------------------

statement 1

GCF = 5 ---> we cannot know if there are bigger prime factors that aren't CF.

insufficient

statement 2

LCM = 105 = 7*3*5

so the biggest prime factor is 7

sufficient

the answer as Fistail wrote is (B)

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Joined: 09 Sep 2013
Posts: 11029
Re: If n and t are positive integers, what is the greatest prime  [#permalink]

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16 Jul 2017, 05:57
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Re: If n and t are positive integers, what is the greatest prime   [#permalink] 16 Jul 2017, 05:57
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