If an integer n is divisible by both 12 and 15, it must also be divisible by which of the following?

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问题 If an integer n is divisible by both 12 and 15, it must also be divisible by which of the following?

选项 A、25
B、16
C、30
D、40
E、70

答案C

解析 12=22×3,15=3×5,而n能够被12和15整除,那么n就至少具有因子22,31,51,选项中哪个数能够由上面因子中的一个或者几个相乘得到,那么这个数就一定能够整除n;25具有两个因子5,不行;16具有4个因子2,也不行;30=2×3×5,2,3,5全部可以为n的因子,因此30一定能够整除n,选择C。
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