求救 2道prep的数学题

the function f is defined for all positive
integers n by the following rule：f(n) is the number of positive integers each of which is less than n
and has no positive factor in common with n other than 1. If p is any prime
number then f(p)=

p-1        
p-2          (p+1)/2       (p-1)/2             2

If x and y are
positive integers, is xy a multiple of 8?

(1)   
the greatest common divisor of x and y is 10.

(2)   
The least common multiple of x and y is 100.

这是DS题，答案是C--both（1）and (2)           我怎么觉得第二个条件就足够了?

1. f(n)代表的是小于N的正整数的个数，且这些正整数与N互质。

因为P是质数，当p＝2，f(p)＝1，意思是小于2且与2互质的只有1。当p＝3，f(p)＝2，意思是小于3且与3互质的有1和2。

依次类推。。。。不知道这样理解对不对。

2.第二个条件可以举4和25，但是4x25不是8的倍数。而20和100的话，20x100就是8的倍数了，所以条件二不足以判断。