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?
Found 3 solutions by lwsshak3, n2, ikleyn:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 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 lowest common denominator of all three numbers=18*14*21=5292 sec or 5292/60=88.2 min
After approximately how many minutes will they come together at the starting point? 88 min
Answer by n2(91) (Show Source):
You can put this solution on YOUR website! .
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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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 =  , (1)
42 =  , (2)
63 =  . (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*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.
Solved.
Answer by ikleyn(53937)  (Show Source):
You can put this solution on YOUR website! .
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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.
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 = , (1)
42 = , (2)
63 = . (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*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.
Compare it with the wrong answer of "88 minutes" in the post by @lwsshar3.
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