prep-T1 DS 170

[hwatai]

170.
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.

[mikesimon]

170.
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.

1) the gretest common factor is 5, so (m,n) could be (10,15) or (35,55), then nt=150 and 1925 each have different prime factor, insufficient.


2) the least common multiple is 105, so (m,n) could be (1,105), (3,35).....and (7,15), then nt will always be 105 , the greatest prime factor is 7, sufficient.

So i choose B......