2. 外语
  3. Both 52 and 33 are factors of n×25×62×73 where n is a positive integer. What is the smallest possible value of n?

Both 52 and 33 are factors of n×25×62×73 where n is a positive integer. What is the smallest possible value of n?

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问题 Both 52 and 33 are factors of n×25×62×73 where n is a positive integer. What is the smallest possible value of n?
选项 A、25
B、27
C、45
D、75
E、125
答案D
解析 n×25×62×73=n×25×(2×3)2×73=n×27×32×73。
要使52和33成为上式的因子，那么n中必然至少含有一个质因子3，两个质因子5，因此n的最小值为52×3=75。
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