document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104299>Question 1104299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ab%5E2c%5E3=3600+ ALIGN=MIDDLE  ALT=\"+ab%5E2c%5E3=3600+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where a, b and c are distinct positive integers greater than 1, what is the least possible value of a+b+c? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719073 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=719073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The prime factorization of 3600 is (2^4)(3^2)(5^2).<br><BR>\n" );
document.write( "If 3600 = ab^2c^3, then c must be 2, because 2 is the only prime factor that occurs 3 or more times.<br><BR>\n" );
document.write( "That means ab^2 = 2(3^2)(5^2).<br><BR>\n" );
document.write( "There are only two possibilities:<BR>\n" );
document.write( "(1) b^2=3^2 and a = 2(5^2) = 50; that makes a+b+c = 50+3+2 = 55; or<BR>\n" );
document.write( "(2) b^2=5^2 and a = 2(3^2) = 18; that makes a+b+c = 18+5+2 = 25.<br><BR>\n" );
document.write( "The minimum value of a+b+c is 25. </SPAN>\n" );
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