document.write( "Question 120756: three strings of a musical instrument vibrate 6,8 and 12 times per second respectively.If all the three begin to vibrate simultaneously,find the shortest time interval before all three vibrate together again? \n" ); document.write( "
Algebra.Com's Answer #88620 by Edwin McCravy(20081)\"\" \"About 
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three strings of a musical instrument vibrate 6,8 and 12 times per second respectively.If all the three begin to vibrate simultaneously,find the shortest time interval before all three vibrate together again?
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\n" ); document.write( "That's the least common multiple of 6, 8, and 12
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\n" ); document.write( "Break each into prime factors:
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\n" ); document.write( "6 = 2x3
\n" ); document.write( "8 = 2x2x2
\n" ); document.write( "12 = 2x2x3
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\n" ); document.write( "2 appears 1 time as a factor of 6, 3 times as a factor of 8
\n" ); document.write( "and 2 times as a factor of 12. That's at most 3 times.
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\n" ); document.write( "Therefore the LCM must contain 2 as a factor the most number of
\n" ); document.write( "times it occurs in any one of those, which is 3 times.
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\n" ); document.write( "3 appears 1 time as a factor of 6, 0 times as a factor of 8
\n" ); document.write( "and 1 time as a factor of 12. That's at most 1 time.
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\n" ); document.write( "Therefore the LCM must contain 3 as a factor the most number of
\n" ); document.write( "times it occurs in any one of those, which is 1 time.
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\n" ); document.write( "Therefore the LCM must contain 2 as a factor 3 times, and
\n" ); document.write( "3 as a factor 1 time. So LCM = 2x2x2x3 = 24
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\n" ); document.write( "Answer: 24 seconds
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\n" ); document.write( "Edwin\r
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