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

@JOTHI

2/ 252 308 198=126 154 99,
2/ 126 154 99= 63 77 99,
7/ 63 77 99,
11/ 9 11 9,
9/ 9 1 9 = 1 1 1,
2 * 2 * 7 * 9 * 11 = 2772.
2772 sec. i.e., 46 min. 12 sec.

When to take lcm and when the hcf? Please explain it clear.

We take lcm because the point of time they meet, will be exactly divisible by their individual timings. 2772 is the smallest number divisible(that is when they first meet).
That is their lcm.
2772/60= 46.2 mints.
.2 mints = 12 seconds (.2*60).

So, the answer is 46 minutes 12 seconds.

Very helpful, Thank you all.

2400 sec= 40min and 360 sec = 6 min. Remaining 12 sec (2400+360+12).

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.

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?

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.

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.

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