document.write( "Question 839386: What is the smallest natural number divisible by each of the integers 1-10, inclusive? \n" ); document.write( "
Algebra.Com's Answer #506119 by Edwin McCravy(20059)\"\" \"About 
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document.write( "We want the least common multiple LCM of those integers,\r\n" );
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document.write( "often written LCM(1,2,3,4,5,6,7,8,9,10)\r\n" );
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document.write( "Every integer is divisible by 1, so we don't need to consider it.\r\n" );
document.write( "We break into primes all the integers 2 through 10\r\n" );
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document.write( "2 prime\r\n" );
document.write( "3 prime\r\n" );
document.write( "4 = 2×2\r\n" );
document.write( "5 prime\r\n" );
document.write( "6 = 2×3\r\n" );
document.write( "7 prime\r\n" );
document.write( "8 = 2×2×2\r\n" );
document.write( "9 = 3×3\r\n" );
document.write( "10 = 2×5 \r\n" );
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document.write( "It must have every one of those primes as a factor as many\r\n" );
document.write( "times as it is a factor of ANY one of those above.\r\n" );
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document.write( "We go through the primes to see how many of each we need for\r\n" );
document.write( "the LCM to have:\r\n" );
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document.write( "2 must be included as a factor 3 times because the most number \r\n" );
document.write( "of times it occurs as a factor of any of those above is 3 times, \r\n" );
document.write( "since 8 contains factor 2 3 times.\r\n" );
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document.write( "So far the LCM must have factors 2×2×2. \r\n" );
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document.write( "3 must be included as a factor 2 times because the most number \r\n" );
document.write( "of times it occurs as a factor of any of those above is 2 times, \r\n" );
document.write( "since 9 contains factor 3 2 times. \r\n" );
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document.write( "So far the LCM must have factors 2×2×2×3×3.\r\n" );
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document.write( "5 must be included as a factor 1 time because the most number \r\n" );
document.write( "of times it occurs as a factor of any of those above is 1 time, \r\n" );
document.write( "once in 5, and once in 10. \r\n" );
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document.write( "So far the LCM must have factors 2×2×2×3×3×5.\r\n" );
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document.write( "7 must be included as a factor 1 time because the most number \r\n" );
document.write( "of times it occurs as a factor of any of those above is 1 time, \r\n" );
document.write( "only once in 7.\r\n" );
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document.write( "That's the last prime, so the LCM must be the product of \r\n" );
document.write( "factors 2×2×2×3×3×5×7 = 2520.\r\n" );
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document.write( "Edwin
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