SOLUTION: If a,b,and c are positive integers, find the sum a+b+c if {{{ a^3bc = 7776 }}} and {{{ ab^3c=17496 }}} and {{{ abc^3=3456 }}}

Question 1188519: If a,b,and c are positive integers, find the sum a+b+c if and and
Answer by Shin123(626) (Show Source): You can put this solution on YOUR website!
Multiplying all 3 equations together, you get .
If we take the prime factorizations of the numbers, we get

.
Multiplying that together, we get .
Taking the 5th root, we get .
Taking the first equation and dividing the equation we just derived, we get .
Doing the same for the other two, we get and .
Since ,,and are positive integers, we have that ,, and .
Adding all of them up, we get .
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