A fruit seller has oranges, apples, and bananas in the ratio \(3:6:7\). If the number of oranges is a multiple of both 5 and 6, then the minimum number of fruits the seller has is:

The minimum is 160 fruits. The smallest positive count of oranges divisible by both 5 and 6 is $\operatorname{lcm}(5,6)=30$, so the scale factor for the ratio is $30/3=10$. The total is $(3+6+7)\times10=160$, whereas 96 uses a scale factor of 6 and gives 18 oranges, which fails the divisibility condition for 5.