document.write( "Question 1079608: find the greatest four digit number which on being divided by 6,12,18,24,and 30 leaves remainder 4 in each case \n" ); document.write( "
Algebra.Com's Answer #693839 by Edwin McCravy(20054)\"\" \"About 
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document.write( "The LCM of 6,12,18,24,30 is 360, so the only positive integers that\r\n" );
document.write( "will leave remainder 4 when divided by all of those is 4 more than\r\n" );
document.write( "a multiple of 360.  Such a number would be of the form 360n+4.\r\n" );
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document.write( "  1000 ≦ 360n+4 ≦ 9999\r\n" );
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document.write( "Subtract 4 from all three sides:\r\n" );
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document.write( "    996 ≦ 360n ≦ 9995\r\n" );
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document.write( "Divide all three sides by 360:\r\n" );
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document.write( "2.7666... ≦ n ≦ 27.763888... \r\n" );
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document.write( "Since n is an integer:\r\n" );
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document.write( "       3 ≦ n ≦ 27\r\n" );
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document.write( "So the smallest such 4 digit number is when n=3, 360*3+4 = 1084.\r\n" );
document.write( "And the greatest such 4 digit number is when n=27, 360*27+4 = 9724.\r\n" );
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document.write( "Answer: 9724.\r\n" );
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document.write( "Edwin
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