由1/a+1/b=1/15 易得 a>15,b>15
1/a=1/15-1/b=(b-15)/15b
a=15b/(b-15)=15+225/(b-15)
因为a、b是自然数
225共有9个约数：1, 3, 5, 9, 15, 25, 45, 75, 225
当b-15分别取1, 3, 5, 9, 15, 25, 45, 75, 225时,
b=16, 18, 20, 24, 30, 40, 60, 90, 240
a=240,90, 60, 40, 30, 24, 20, 18, 16
故a+b的最大值是256,最小值是60