# 140 Followers Problem - 2

$\Large \lfloor \log (x) \rfloor + \lfloor \log (y) \rfloor + \lfloor \log (z) \rfloor = 140$

If the number of positive integral solutions to above equation can be expressed in the form of $$a^{b}\times c^{d} \times e^{f} \times g^{h} \times i^{j}$$, where $$a$$, $$c$$, $$e$$, $$g$$ and $$i$$ are distinct positive primes and $$b$$, $$d$$, $$f$$, $$h$$ and $$j$$ are positive integers. Then find the value of

$a+b+c+d +e+f+g+h+i+j$

Details and Assumptions

• $$\lfloor k \rfloor$$ represents the greatest integer less than or equal to $$k$$.

• $$\log k$$ is the logarithm of $$k$$ to the base 10.

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