If n and t are positive integers, what is the greatest prime factor of nt?

1). The greatest common factor of n and t is 5

2). The least common multiple of n and t is 105



(1) this only tells is that the greatest number that is in both factorizations - those of n and t - is 5. but there could be a larger factor that is part of only one of the factorizations. for instance:
- it's possible that n = t = 5. then the greatest prime factor of nt is 5.
- it's possible that n = 5 and t = 35. then the greatest prime factor of nt is 7.
insufficient.

(2) the least common multiple contains every factor of t or n at least once. (it has to; if, say, t had a factor that wasn't contained in it, then it would fail to be a multiple of t.) so, the biggest prime factor of this # will also be the biggest prime factor of the product nt.
sufficient.
try a few combinations of n and t if you aren't convinced.

answer = b