document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=822570>Question 822570</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The least number when divided by 0.06, 0.008 and 0.16 gives integers as quotient is- </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #494999 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=494999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think the solution will be easier to understand if we rewrite the decimals as fractions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.06+=+6%2F100+=+3%2F50 ALIGN=MIDDLE  ALT=\"0.06+=+6%2F100+=+3%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.008+=+8%2F1000+=+1%2F125 ALIGN=MIDDLE  ALT=\"0.008+=+8%2F1000+=+1%2F125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.16+=+16%2F100+=+4%2F25 ALIGN=MIDDLE  ALT=\"0.16+=+16%2F100+=+4%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Let x be the desired number. Then<ul><li>x divided by 3/50 is an integer.</li><li>x divided by 1/125 is an integer.</li><li>x divided by 4/25 is an integer.</li></ul>Since dividing by a fraction is done by multiplying by the fraction's reciprocal:<ul><li>x times 50/3 is an integer.</li><li>x times 125/1 is an integer.</li><li>x times 25/4 is an integer.</li></ul>If all these multiplications are integers, then the factors of each denominator <u>must</u> be canceled by factors of x. So let's look at the factors of the denominators (of the reciprocals):<BR>\n" );
document.write( "3 = 3 * 1<BR>\n" );
document.write( "1 = 1 * 1<BR>\n" );
document.write( "4 = 2 * 2<br><BR>\n" );
document.write( "Since 1 is a factor of everything, x must only have one 3 and two 2's as factors in order for it to cancel the factors of each of the denominators. (any additional factors will just make x larger.) So:<BR>\n" );
document.write( "x = 3 * 2 * 2 = 12 </SPAN>\n" );
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