Question

A,B,C,D start at the same time to run around a circular garden in the same direction .A completes a round in 30 minutes,B in 60 minutes,c in 90 minutes and D in 105 minutes.after what time will they meet again at the starting point

Answer 1

you should find lcm(30, 60, 90, 105)

Answer 2

is it 15

Answer 3

if i tell i will be banned

Answer 4

but it isn't

Answer 5

k.5,3,3,4,3,7 is the lcm ., as multiply=3280

Answer 6

@pooja123 , when you say 15 you are thinking of GCF (greatest common factor). You want LCM - LCM is ALWAYS at least as LARGE as the largest number.

Answer 7

nope, dude you should take 3 only one time

Answer 8

k.5,3,7 ,4=420min

Answer 9

420 divided by 90 =?

Answer 10

There is a brute force way to find LCM, and an algorithmic way.

Brute force: list multiples of each number, until you find the smallest number that is common to all. Can be tedious with several numbers.

Algorithmic way: do the prime factorization of each number. Then "cook up" the GCF as the product of ALL the factors, the MOST number of times they appear in any of the factorizations.

Answer 11

E.g., if I want the LCM of 40,50 I do the prime factors of each:

40=2*2*2*5
50=2*5*5

Then my LCM need to have three factors of 2, and two factors of 5:
LCM=2*2*2*5*5=200

Answer 12

Now apply that to your four numbers above. It is guaranteed to work every time. :)

Answer 13

k.i got it.

Answer 14

okeydoke, good.

Answer 15

2,3,5,7=210

Answer 16

sry 3^2,2^2,5,7=1860

Answer 17

no. you have an extra factor of 2 there, and your product isn't right regardless (e.g., you don't get 1860 from that product).

Answer 18

You only need 1 factor of 2, because none of the numbers have 4 as a factor.

Answer 19

Did you do the prime factorizations? (And really, since 90 is a multiple of 30 and 60, you ONLY need to find GCF(90,105), the factors of 30 and 60 are all included in the factors of 90)

Answer 20

210

Answer 21

So really, you just need 90 * (any factors of 105 that are NOT factors of 90)

Answer 22

No, too small. 90 is not a factor of 210.

Answer 23

If you show me your work, I can help you understand why it isn't working. If you follow the algorithm I've explained, it will work.

Answer 24

Give the prime factorizations of:

90:
105:

Answer 25

30=3.2.5
60=3.2.25
90=3.2.3.5
105=3.7.5

Answer 26

Oh crap... you're right, I was forgetting about the 2*2 in 60. lol duh to me.

So it does not reduce to LCM(90,105) as I said, but it does reduce to LCM(60,90,105) - you can basically ignore the 30 because any multiple of 60 or 90 is also a multiple of 30.

Answer 27

1260

Answer 28

Right.... your set up above
3^2,2^2,5,7=1860
is right, just the result was wrong.

Sorry about my "4" snafu! But you have the right idea now. : )

Answer 29

k.thanks a lot

Answer 30

you're welcome. :)