document.write( "Question 279896: The people at a meeting of Goodtime Sports are forming equal teams. When they form groups of 2, 3, 4, 5, or 6 there is always exactly one person left. What is the smallest number of people that could be at the meeting?
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Algebra.Com's Answer #203429 by Edwin McCravy(20065)\"\" \"About 
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The people at a meeting of Goodtime Sports are forming equal teams. When they form groups of 2, 3, 4, 5, or 6 there is always exactly one person left. What is the smallest number of people that could be at the meeting?
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document.write( "One more than any multiple of p, say qp, will \r\n" );
document.write( "leave a remainder of 1 when divided by p.\r\n" );
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document.write( "Proof:\r\n" );
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document.write( "   q\r\n" );
document.write( " -------\r\n" );
document.write( "p)qp + 1\r\n" );
document.write( "  qp\r\n" );
document.write( "  --\r\n" );
document.write( "       1\r\n" );
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document.write( "Conversely, if a remainder of 1 is left when integer\r\n" );
document.write( "n is divided by p, then n is one more than a mutiple of p.\r\n" );
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document.write( "Proof:\r\n" );
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document.write( "Suppose\r\n" );
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document.write( "   q\r\n" );
document.write( " -----\r\n" );
document.write( "p) n\r\n" );
document.write( "  pq\r\n" );
document.write( "  --\r\n" );
document.write( "   1\r\n" );
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document.write( "Then qp+1 = n\r\n" );
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document.write( "Therefore 1 more than the least common multiple of 2, 3, 4, 5, and 6\r\n" );
document.write( "will be the least positive integer that will leave a remainder of 1\r\n" );
document.write( "when any of these are divided into it.\r\n" );
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document.write( "The least common multiple of 2,3,4,5, and 6 is 60, so one more than that,\r\n" );
document.write( "61, is the desired integer.\r\n" );
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document.write( "Edwin
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