Question 955731
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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?
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        The solution and the answer in the post by @lwsshar3 both are incorrect.

        I came to provide a correct solution and to teach you solving this problem 

        and similar problems in a right way.



<pre>
We should find a minimum common multiple of numbers 54, 42 and 63.
It is called also LCM (Least Common Multiple) of numbers 54, 42 and 63.
Standard designation for it is LCM(54,42,63).


For it, we factor (decompose) these numbers into product of prime numbers

    54 = {{{2*3^3}}},    (1)

    42 = {{{2*3*7}}},    (2)

    63 = {{{3^2*7}}}.    (3)


So, the participating prime numbers are 2, 3 and 7.


LCM is the product of these participating prime numbers 2, 3 and 7 in degrees 
which are maximum indexes of these primes in decompositions (1), (2) and (3).


So, for '2' the degree in LCM is max(1,1,0) = 1;

    for '3' the degree in LCM is max(3,1,2) = 3;

    for '7' the degree in LCM is max(0,1,1) = 1.


Thus, LCM(54,42,63) = {{{2^1*3^3*7^1}}} = 2*27*7 = 378.


So, the closest time, when Seema, Meena and Reema will meet together in the starting point is 378 seconds,
or 6 minutes and 18 seconds, which is about 6 minutes, approximately.
</pre>

Compare it with the wrong answer of "88 minutes" in the post by @lwsshar3.