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

LCM is 2772.

So, 2772/60 = 46min 12sec.

Just take LCM of 252, 308 & 198.

LCM = 2772 seconds or 46 minutes 12 seconds.

@All.

Simple solution:

The L C M of given number = 2772
=> 2772 ÷ 60 we get 46 as quotient and 12 as a reminder.

Thanks for all the given explanation.

Thank you all for explaining the answer.

Can you kindly explain in details because I don't understand? Please help me to get it.

1. Decompose all numbers into prime factors.
198 2
99 3
33 3
11 11
1

252 2
126 2
63 3
21 3
7 7
1

308 2
154 2
77 7
11 11
1

2. Write all numbers as the product of its prime factors
Prime factors of 198 = 2 . 32 . 11
Prime factors of 252 = 22 . 32 . 7
Prime factors of 308 = 22 . 7 . 11

3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 2
Common prime factors with the greatest exponent: 22
Uncommon prime factors: 3 , 11 , 7
Uncommon prime factors with the greatest exponent: 32, 111, 71

4. Calculate the Least Common Multiple or LCM
Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.
LCM = 22. 32. 111. 71 = 2772 1. Decompose all numbers into prime factors

198 2
99 3
33 3
11 11
1

252 2
126 2
63 3
21 3
7 7
1

308 2
154 2
77 7
11 11
1

2. Write all numbers as the product of its prime factors

Prime factors of 198 = 2 . 32 . 11
Prime factors of 252 = 22 . 32 . 7
Prime factors of 308 = 22 . 7 . 11

3. Choose the common and uncommon prime factors with the greatest exponent

Common prime factors: 2
Common prime factors with the greatest exponent: 22
Uncommon prime factors: 3 , 11 , 7
Uncommon prime factors with the greatest exponent: 32, 111, 71

4. Calculate the Least Common Multiple or LCM.
Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.

LCM = 22. 32. 111. 71 = 2772= 46 minutes 12 seconds.

A complete his round in 252 seconds.
B completes his round in 308 seconds.
C completes his round in 198 seconds.

They will agian at starting together after,
LCM of 252, 308 and 198.
252 = 2 *2 *3*3*7
308 = 2 *2*7*11
198 = 2 *3*3*11
Required LCM = 2*2*3*3*7*11 = 2772 seconds = 46 minutes 12 seconds.

Three girls starting jogging from the same point around a circular track each one complete one round in 24 sec, 36 sec, 48 sec. Respectively after how much time will they meet at one point? Can anyone solve this?

I didn't get the same answer (46.12 second). I got only 46.2 second.

How you got 46.12 seconds?

I divided 2772 /60 then I got 46.2 second.