SOLUTION: If {{{ ab^2c^3=3600 }}}, where a, b and c are distinct positive integers greater than 1, what is the least possible value of a+b+c?

Question 1104299: If , where a, b and c are distinct positive integers greater than 1, what is the least possible value of a+b+c?
Found 2 solutions by greenestamps, stanbon:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The prime factorization of 3600 is (2^4)(3^2)(5^2).

If 3600 = ab^2c^3, then c must be 2, because 2 is the only prime factor that occurs 3 or more times.

That means ab^2 = 2(3^2)(5^2).

There are only two possibilities:
(1) b^2=3^2 and a = 2(5^2) = 50; that makes a+b+c = 50+3+2 = 55; or
(2) b^2=5^2 and a = 2(3^2) = 18; that makes a+b+c = 18+5+2 = 25.

The minimum value of a+b+c is 25.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If , where a, b and c are distinct positive integers greater than 1, what is the least possible value of a+b+c?
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3600/8 = 450
450/9 = 50
===
a = 50
b = 3
c = 2
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Cheers,
Stan H.
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