Answer:
So:
Counting from a given time t = 0min, we know that:
Each 15 mins she removes the scones
Each 12 mins she removes the muffins
Each 10 mins she removes the cookies.
So when will she remove both at the same time?
Well, this will happen in the smallest common multiple of 15, 12 and 10.
or at LCM(10, 12, 15).
How we find it?
well, in this case is easy.
All the multiples of 10 end with a zero.
So let's find the multiples of 12 and 15 that also end with a zero:
12*6 = 60
15*4 = 60
and
10*6 = 60
So the LCM(10,12,15) = 60.
Another way is by calculating:
10*12*15/(GCF(10,12)*GCM(12,15)*GCM(10,15)
Where GCF = greatest common factor.
Between 10 and 12 is 2.
Between 12 and 15 is 3
Between 10 and 15 is 5.
Then:
10*12*15/(2*3*5) = 60.
This means that 60 minutes after she starts, she will remove the scones, muffins and cookies at the same time.
