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ChoiceCollect

1. 1-1500, 除去2,5,7的倍数,还剩几个数

思路:为2,5,7的倍数的个数总共有n个,求n。
(1)2的倍数:1500/2=750个
    5的倍数:1500/5=300个
    7的倍数:1500/7(下取整)=214个
    750+300+214=1264
(2)2和5的最小公倍数,10的倍数:1500/10=15个
    2和7的最小公倍数,14的倍数:1500/14=107个
    5和7的最小公倍数,35的倍数:1500/35=42个
    去掉(1)中算重复的,1264-15-107-42=1100
(3)2,5和7的最小公倍数,70的倍数:1500/70=21个
   说明:70在(1)中加了3次,在(2)中减了3次,所以2,5,7的最小公倍数的倍数还需再加上一次
   n=1100+21=1121
则,还剩1500-n=1500-1121=379个。

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