If x, y, and z are positive integers and 2x=3y=5z=7w, then the least possible va

游客2025-02-23 26

问题 If x, y, and z are positive integers and 2x=3y=5z=7w, then the least possible value of x+y+z+w is

选项 A、70
B、42
C、105
D、247
E、30

答案 D

解析要求x+y+z+w的最小值，必须每一项都取最小值。对于x来说，2x=3y=5z=7w，那么x必然具有因子3，5，7，因此x的最小值为3×5×7=105；同理y的最小值为2×5×7=70，z的最小值为2×3×7=42，w的最小值为2×3×5=30，所以x+y+z+w的最小值为105+70+42+30=247。正确答案为D。

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