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If x, y, and z are positive integers and 2x=3y=5z=7w, then the least possible va
If x, y, and z are positive integers and 2x=3y=5z=7w, then the least possible va
游客
2024-01-13
46
管理
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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