Question

Kaitlyn is making big goods for charity bake sale he places a tray of scones a tray of muffins and a tray of cookies in the oven discounts bake for 15 minutes the muffins bake for 12 minutes and the cookies bake for 10 minutes when one trays done he removes it and replace it with another tray at the same I don't how many minutes after kaylan put the trays in the oven when he 1st remove the scones muffins and cookies at the same time

Answer 1

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.