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Greatest prime factor

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by josh80 » Wed Dec 11, 2013 3:58 pm
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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Source: — Data Sufficiency |
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by theCodeToGMAT » Thu Dec 12, 2013 12:15 am
To find: Greatest prime Factor of nt

Statement 1:
n = 5 x _
t = 5 x _
here, we don't know whether we have greater Prime factor than "5" in the "_".
INSUFFICIENT


Statement 2: LCM = 105 = 7 x 3 x 5
here, we are sure that n & t will have these 3 numbers..
So, "7" is the Greatest Prime Factor
SUFFICIENT

Answer [spoiler]{B}[/spoiler]
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by Matt@VeritasPrep » Thu Dec 12, 2013 5:24 pm
Just to follow up on Rahul's remark, the key concept here is that the LCM of two numbers will always contain the unique prime factors of each of those numbers (and NO other prime factors).

For instance, say I want the LCM of 14 and 30. Since the LCM has to divide by 14, it has to divide by 2 * 7. Since the LCM has to divide by 30, it has to divide by 2 * 3 * 5. So the LCM is 2 * 3 * 5 * 7, and the greatest prime factor (7) is the greatest prime factor found in either 14 or 30.
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