document.write( "Question 134110: If a 75-degree sector rotates around the center of a cirlce in 75-degree movements, how many sector movements will be needed for the sector to land in its original postition? \n" ); document.write( "

Algebra.Com's Answer #98081 by Earlsdon(6294) $\"\"$ $\"About$

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What you are really asking for here is the least common multiple (LCM) of 75 and 360.
\n" ); document.write( "You can do this by first finding the prime factors of each of the numbers.
\n" ); document.write( " $\"75+=+2%2A5%2A5\"$
\n" ); document.write( " $\"360+=+2%2A2%2A2%2A3%2A3%2A5\"$
\n" ); document.write( "Now where you have repeated factors, write them in exponential form:
\n" ); document.write( " $\"75+=+2%2A5%5E2\"$
\n" ); document.write( " $\"360+=+2%5E3%2A3%5E2%2A5\"$
\n" ); document.write( "Then, from each list, select the highest power of each factor and multiply these together to get the LCM:
\n" ); document.write( " $\"LCM+=+2%5E3%2A3%5E2%2A5%5E2\"$
\n" ); document.write( " $\"LCM+=+1800\"$
\n" ); document.write( "Answer: 1800 movements will be needed for the sector to land in its original position. \n" ); document.write( "

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