document.write( "Question 955731: Seema, Meena and Reema begin to jog around a circular stadium and they complete their revolutions in 54 seconds, 42 seconds and 63 seconds respectively. After approximately how many minutes will they come together at the starting point? \n" ); document.write( "

Algebra.Com's Answer #854598 by n2(91) $\"\"$ $\"About$

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\n" ); document.write( "Seema, Meena and Reema begin to jog around a circular stadium and they complete their revolutions in 54 seconds,
\n" ); document.write( "42 seconds and 63 seconds respectively. After approximately how many minutes will they come together
\n" ); document.write( "at the starting point?
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document.write( "We should find a minimum common multiple of numbers 54, 42 and 63.\r\n" );
document.write( "It is called also LCM (Least Common Multiple) of numbers 54, 42 and 63.\r\n" );
document.write( "Standard designation for it is LCM(54,42,63).\r\n" );
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document.write( "For it, we factor (decompose) these numbers into product of prime numbers\r\n" );
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document.write( "    54 = ,    (1)\r\n" );
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document.write( "    42 = ,    (2)\r\n" );
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document.write( "    63 = .    (3)\r\n" );
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document.write( "So, the participating prime numbers are 2, 3 and 7.\r\n" );
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document.write( "LCM is the product of these participating prime numbers 2, 3 and 7 in degrees \r\n" );
document.write( "which are maximum indexes of these primes in decompositions (1), (2) and (3).\r\n" );
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document.write( "So, for '2' the degree in LCM is max(1,1,0) = 1;\r\n" );
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document.write( "    for '3' the degree in LCM is max(3,1,2) = 3;\r\n" );
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document.write( "    for '7' the degree in LCM is max(0,1,1) = 1.\r\n" );
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document.write( "Thus, LCM(54,42,63) =  = 2*27*7 = 378.\r\n" );
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document.write( "So, the closest time, when Seema, Meena and Reema will meet together in the starting point is 378 seconds,\r\n" );
document.write( "or 6 minutes and 18 seconds, which is about 6 minutes, approximately.\r\n" );
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