document.write( "Question 207599: Find the greatest number of four digits which when increased by 1 is exactly divisible by 2,3 ,4,5,6 and 7. \n" ); document.write( "

Algebra.Com's Answer #156984 by Edwin McCravy(20060) $\"\"$ $\"About$

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Find the greatest number of four digits which when increased by 1 is exactly divisible by 2,3 ,4,5,6 and 7.
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document.write( "For a positive integer to be divisible by those\r\n" );
document.write( "it must divisible by their Least common multiple:\r\n" );
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document.write( "We find the least common multiple of 2,3,4,5,6, and 7\r\n" );
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document.write( "Break each into primes if it is not prime\r\n" );
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document.write( "2=2\r\n" );
document.write( "3=3\r\n" );
document.write( "4=2*2\r\n" );
document.write( "5=5\r\n" );
document.write( "6=2*3\r\n" );
document.write( "7=7\r\n" );
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document.write( "so LCM = 2*2*3*5*7 = 420 \r\n" );
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document.write( "Every multiple of 420 is divisible by all those above.\r\n" );
document.write( "Every multiple of 420 can be written 420n, where\r\n" );
document.write( "n is an integer. The largest 4-digit integer is\r\n" );
document.write( "9999. Therefore: \r\n" );
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document.write( "Since n is an integer\r\n" );
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document.write( "Therefore the largest multiple of 420\r\n" );
document.write( "which has 4 digits is 420*23 or 9660.\r\n" );
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document.write( "However the problem asked for the largest digit\r\n" );
document.write( "that when increased by 1 will give 9660. Obviously\r\n" );
document.write( "this is 1 less than 9660, or 9659.\r\n" );
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document.write( "Answer = 9659.\r\n" );
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document.write( "Edwin

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