document.write( "Question 968712: The HCF and LCM of two positive
\n" ); document.write( "integers are 35 and 385 respectively.
\n" ); document.write( "If one of the integers is 77, what is
\n" ); document.write( "the other integer? \n" ); document.write( "

Algebra.Com's Answer #591926 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
The HCF and LCM of two positive
\n" ); document.write( "integers are 35 and 385 respectively.
\n" ); document.write( "If one of the integers is 77, what is
\n" ); document.write( "the other integer?
\n" ); document.write( "

\r\n" );
document.write( "Something's wrong!  35 is NOT a factor of 77, so it cannot be the \r\n" );
document.write( "the HCF of 77 and any other number since it's not even a factor of 77.\r\n" );
document.write( "If your teacher gave you 77, you must point it out to him/her that\r\n" );
document.write( "35 is not a factor of 77, thus 35 cannot be the HCF of it and any \r\n" );
document.write( "other positive integer. \r\n" );
document.write( "-----------------\r\n" );
document.write( "\r\n" );
document.write( "But I won't leave you hanging:\r\n" );
document.write( "\r\n" );
document.write( "Here is a similar problem that makes sense:\r\n" );
document.write( "\r\n" );
document.write( "The HCF and LCM of two positive integers are 12 and 5544 respectively.\r\n" );
document.write( "If one of the integers is 264, what is the other integer.\r\n" );
document.write( "\r\n" );
document.write( "We know that 264, 5544, and the unknown integer are all multiples of 12.\r\n" );
document.write( "\r\n" );
document.write( "We divide 5544 by 12, getting 462, which contains all the prime factors of \r\n" );
document.write( "5544 as many times as and no more than they are contained in both 264 and the\r\n" );
document.write( "unknown integer.\r\n" );
document.write( "\r\n" );
document.write( "We divide 264 by 12, getting 22, which must contain all but only those\r\n" );
document.write( "prime factors of 5544 that are contained in 264 but not in the unknown\r\n" );
document.write( "integer. \r\n" );
document.write( "\r\n" );
document.write( "We reason:\r\n" );
document.write( "462 must contains all the prime factors of the unknown integer that\r\n" );
document.write( "22 does not contain as prime factors.\r\n" );
document.write( "\r\n" );
document.write( "So we divide 462 by 22, getting 21, which contains all those,\r\n" );
document.write( "and only those, factors of 12 that 264 does not contain.\r\n" );
document.write( "\r\n" );
document.write( "Therefore the unknown integer has to be a multiple of\r\n" );
document.write( "as those factors of 5544 which 264 does not contain, so it\r\n" );
document.write( "must be 21*12 = 252\r\n" );
document.write( "\r\n" );
document.write( "------------------\r\n" );
document.write( "Here is a formula for this kind of problem:\r\n" );
document.write( "\r\n" );
document.write( "The HCF and LCM of two positive\r\n" );
document.write( "integers are H and L respectively.\r\n" );
document.write( "If one of the integers is A, what is\r\n" );
document.write( "the other integer B?\r\n" );
document.write( "\r\n" );
document.write( "B = [(L÷H)÷(A÷H)]H\r\n" );
document.write( "\r\n" );
document.write( "If you have any questions, feel free to ask them in the \r\n" );
document.write( "thank-you note form below.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );