【急问】一道数学题 pp2里面的

the integers m and p are such that 2<m<p and m is not a factor of p.
if r is the remainder when p is divided by m, is r>1?
1.the greatest common factor of m and p is 2.
2.the least common multiple of m and p is 30.

我觉得由2可以得出r=1

所以选D

可是答案是A

为什么呢？谢谢！

agree

there are only two cases meet all demands

2<5<6 r=1

2<3<10 r=1

我的想法是这样

1.the greatest common factor of m and p is 2.

那 m, p 一定都是2的倍数 又 2<m<p 而且  m is not a factor of p (如果是的话那r有可能是0)

==> r 一定会大于1 (ex. 6/4, 8/6) 充分

2.the least common multiple of m and p is 30.

同意可推得 2<5<6 r=1,2<3<10 r=1 ==>  r>1? no

同意 m=10,p=15,then the remaider is 5 ==> r>1? yes 不充分