∵ a^x=b^y=c^z=30^w
∴ a=30^(w/x),b=30^(w/y),c=30^(w/z)
∵ 1/x + 1/y + 1/z = 1/w
∴ w/x + w/y + w/z = 1
∴ abc = 30^(w/x + w/y + w/z) = 30^1 = 30
∵ a、b、c是正整数
∴ {a,b,c} = {2,3,5}或{1,2,15}{1,3,10}{1,5,6}
又∵当a,b,c其中有一个为1时,1=a^x=b^y=c^z=30^w,w=0,与w是分母矛盾
∴ {a,b,c} = {2,3,5},且由a≤b≤c知
a=2,b=3,c=5