document.write( "Question 593989: The L.C.M of two numbers is 120 and their G.C.F is 6. one of the numbers is 30, what is the other number?
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Algebra.Com's Answer #376592 by Edwin McCravy(20086) $\"\"$ $\"About$

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The L.C.M of two numbers is 120 and their G.C.F is 6. one of the numbers is 30, what is the other number?
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document.write( "Easy way:\r\n" );
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document.write( "The product of the GCF and the LCM of two numbers is the product of the two numbers\r\n" );
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document.write( "Let the other number be N.\r\n" );
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document.write( "Then GCF×LCM = 30N or\r\n" );
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document.write( "      6(120) = 30N\r\n" );
document.write( "         720 = 30N\r\n" );
document.write( "          24 = N\r\n" );
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document.write( "HARDER WAY but involves thinking not a memorized formula:\r\n" );
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document.write( " 30 = 2    ×3×5\r\n" );
document.write( "  ? = ?  \r\n" );
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document.write( "      2    ×3   = 6\r\n" );
document.write( "      2×2×2×3×5 = 120\r\n" );
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document.write( "Rule for L.C.M\r\n" );
document.write( "The L.C.M. of two positive integers must have a prime factor \r\n" );
document.write( "the MOST number of times which ONE of them has it as a factor. \r\n" );
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document.write( "Ruke for G.C.F\r\n" );
document.write( "The G.C.F. of two positive integers must have a prime factor \r\n" );
document.write( "the LEAST number of times which BOTH of them have it as a factor.\r\n" );
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document.write( "L.C.M. = 120 has 2 as a factor three times, so the MOST number \r\n" );
document.write( "of times 30 or the other number has it as a factor is three times.\r\n" );
document.write( "30 only has 2 as a factor 1 time, so the other number must have 2\r\n" );
document.write( "as a factor 3 times.  So the other number is at least 2×2×2\r\n" );
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document.write( "G.C.F. = 6 has 2 and 3 once each as its prime factors.  30 has both these\r\n" );
document.write( "factors once so the other number must have both of them once, so the other\r\n" );
document.write( "number must have factor 2 and 3.\r\n" );
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document.write( "We have already determined that it must have 2 as a factor, (in fact it\r\n" );
document.write( "must have it three times); therefore the other number has 2 as a factor \r\n" );
document.write( "3 times and 3 as a factor once.\r\n" );
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document.write( "So the other number is 2×2×2×3 = 24.\r\n" );
document.write( "Infact you can fill it in from this chart:\r\n" );
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document.write( " 30 = 2    ×3×5\r\n" );
document.write( "  ? = ?  \r\n" );
document.write( "---------------\r\n" );
document.write( "      2    ×3   = 6\r\n" );
document.write( "      2×2×2×3×5 = 120\r\n" );
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document.write( "Bring up the factor not represented by one of the numbers \r\n" );
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document.write( " 30 = 2    ×3×5\r\n" );
document.write( " 24 = 2×2×2×3  \r\n" );
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document.write( "      2    ×3   = 6\r\n" );
document.write( "      2×2×2×3×5 = 120\r\n" );
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document.write( "Edwin

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