It is known that the decomposed prime factor of a positive integer A can be written as A=2α*3β*5γ, where α, β, γ are natural numbers. If one-half of A is a perfect square number, one-third of A is a perfect cubic number, and one-fifth of A is the fifth power of a natural number, then what is the minimum value of α+β+γ
已知正整数A分解质因数可以写成A=2α*3β*5γ，其中α、β、γ是自然数．如果A的二分之一是完全平方数，A的三分之一是完全立方数，A的五分之一是某个自然数的五次方，那么α+β+γ的最小值是多少
<gadget id="calculator">15 + 6 + 10</gadget>
<output>31</output>

<result>31</result>