Aptitude - Problems on H.C.F and L.C.M - Discussion

Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 15)
15.
A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?
26 minutes and 18 seconds
42 minutes and 36 seconds
45 minutes
46 minutes and 12 seconds
Answer: Option
Explanation:

L.C.M. of 252, 308 and 198 = 2772.

So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.

Discussion:
66 comments Page 1 of 7.

Hassan Raza said:   3 years ago
2772/60 = quotient = 46 ---> Minutes.
Remainder= 12----> second,
Thus, 46 minutes 12 second.
(10)

Vandan said:   4 years ago
It's simple, we have to only take out lcm which is 2772 and then convert it into time.
(2)

Luci said:   4 years ago
@Giridhar.

Can you explain in more detail? Please.
(1)

Giridhar said:   4 years ago
Here 252,308,198.
Choose the biggest number.

308 check whether divisible by other 2 numbers i.e 252 and 198.
If not check for factors of 308 that would be lcm,
308/252 = 1.22.
308/198 = 1.55.
multiple of 308.

308*2.
Check further finally 308 * 9=2772.
2772/252 = 11.
2772/198 = 14.

Finally the answer is 2772 i.e 46min 12sec.
(11)

Akhila said:   4 years ago
@Isa.

Your answer is very helpful. Thank you'.
(5)

Madhan said:   4 years ago
2 [252,308,198]
2[126,154,99]
3[63,77,99]
3[21,77,33]
7[7,77,11]
11[1,11,11]
[1,1,1]
2*2*3*3*7*11=2772

Here, 60 sec = 1 minute.
Hence,
Simply divide 2772/60.
You will get 46.
And remainder 12.
Here, the remainder is seconds.
(30)

Ramin said:   4 years ago
Simply divide 2772 by 60.
You will get 46.
And remainder 12.
The remainder is seconds.
(3)

Isha said:   5 years ago
Thanks all for explaining the answer.
(1)

Virat said:   5 years ago
Just deduce it like this---->>

252 ---2*126 = 2^2*63 = 2^2*3*21 = 2^2*3^2*7.
308 ---2*154 =2^2*77 = 2^2*11*7.
198 ---2*99 = 2*3*11.
Now just take the prime factors with the highest power out.
So LCM = 2^2*3^2*7*11= 2772.
(4)

Anyone said:   6 years ago
I have not understand what you said please show me the LCM how you have done.
(2)


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