document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1064777>Question 1064777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the smallest number that when divided by 2, 3, 4, 5, or 6, it leaves a remainder of one but when divided by 7 has no remainder.\r<BR>\n" );
document.write( "\n" );
document.write( "my work:\r<BR>\n" );
document.write( "\n" );
document.write( "So I first I found the LCM of 2, 3, 4, 5, 6 which is 60.\r<BR>\n" );
document.write( "\n" );
document.write( "Then I added 1 to 60 which is 61.\r<BR>\n" );
document.write( "\n" );
document.write( "Then I multiplied 61 by 7 repeatedly till it fulfilled the condition that remainder should be 1. I got the answer 146461 which seems to correct but not completely sure. \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #679863 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52943)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=679863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Let N be our unknown number under the question.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Consider the number N-1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "According to the condition, it is multiple of 2, 3, 4, 5 and 6.\r\n" );
document.write( "Hence, N-1 is the multiple of 60.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that our N is somewhere among these numbers: \r\n" );
document.write( "\r\n" );
document.write( "60+1, 2*60+1, 3*60+1, 4*60+1, 5*60+1, 6*60+1\r\n" );
document.write( "\r\n" );
document.write( "i.e, among the numbers 61, 121, 181, 241, 301.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Check, which of these numbers is multiple of 7.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "<U>Answer</U>. 301.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "See the lesson\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/The-number-that-leaves-a-remainder-1-when-divided-by-2-by-3-by-4-by-5-and-so-on-until-9.lesson>The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9</A>\r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );