document.write( "Question 563995: what is the least common multiple and the greatest common factor of 125, 235 and 270? \n" ); document.write( "

Algebra.Com's Answer #365184 by KMST(5328) $\"\"$ $\"About$

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The prime factorizations are
\n" ); document.write( " $\"125=5%5E3\"$
\n" ); document.write( " $\"235=5%2A47\"$
\n" ); document.write( " $\"270=2%2A5%2A3%5E3\"$
\n" ); document.write( "The numbers 2, 3, and 47 do not appear in all factorizations.
\n" ); document.write( "The only common factor is $\"5\"$ .
\n" ); document.write( "All three numbers are multiples of $\"5\"$ , but not of $\"5%5E2\"$ , or $\"5%5E3\"$ .
\n" ); document.write( "So, the greatest common factor is 5.
\n" ); document.write( "The factorization of a common multiple must contain at least
\n" ); document.write( " $\"5%5E3\"$ , $\"47\"$ , $\"2\"$ , and $\"3%5E3\"$ ,
\n" ); document.write( "all prime factors with the largest exponents.
\n" ); document.write( "The least common multiple is
\n" ); document.write( "LCM= $\"2%2A3%5E3%2A5%5E3%2A47\"$ =317250
\n" ); document.write( "All the other common multiples are multiples of 317250. \n" ); document.write( "

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