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List A, B and C means the list of multiples of prime numbers 2, 3, and 5 respect
List A, B and C means the list of multiples of prime numbers 2, 3, and 5 respect
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2024-01-13
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问题
List A, B and C means the list of multiples of prime numbers 2, 3, and 5 respectively, how many integers between 1 and 100, inclusive, will apper on all three of the lists?
选项
A、None
B、l
C、3
D、5
E、An infinite number of integers
答案
C
解析
如果这个数出现在三个List中,那么它必然是2,3,5的倍数,因此只要求出1到100有多少个数能够同时整除2,3,5,这三个质数的最小公倍数为2×3×5=30,100=30×3+10,因此有3个能够同时整除2,3,5,所以选择C。
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