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题库 / Prep2007E1-DS-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.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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(1)n,t有多种可能，定不了nt自然定不了最大质数。
(2)n,t 只可能是3,5，7之一或二者或三者相乘，最大不超过105=3*5*7,且nt乘积一定同时包含了3.5.7.才有可能最小公倍数为105.故可推出最大质数:7 回复
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