I will switch every light bulb that's divisible by two.

Well it's going to be a non negative multiple of 3.

Now, once again, you may be able to do it in your head

Every possible value for the amount of money he collects for our function has to be a multiple of 3.

It might be more that that, but it has to be at least three.

Well, sure.

Well what's the least common multiple of two and three?

If t is always going to be a non negative integer, then what's 3t always going to be?

Well that's the smallest number that's a multiple of both two and three.

Well, we say, well, what number times 2 is equal to negative 3?

Well we were able to figure out Jared's age. it is eight.

I grouped the negative 3 with the 21, or the negative 21, because they're both divisible by 3.

Talia's age and they say it they tell it to us right over here.

And 4 and 3 don't share any prime factors with each other.

The first is twice as long as the second.

Now that's the multiples of 15 up through 105. Obviously, we keep going from there. Now lets do the multiples of 6.

I'll do this in magenta

The enemy outnumbers us a paltry three to one.

If the sum of that is a multiple of 3 then this whole thing is a multiple of 3

And 3 it's already a prime number, so you can't prime factorize it any more.

So what you want to do is think of a number that has all of the prime factors of 4 and 3.

It turns out that what we want for, what we'll call the common denominator, it turns out to be the least common multiple of two and three.

The common denominator of 3 4 and 2 3 is going to be the least common multiple of 4 and 3.

Remember, you factor out everything that you can factor out.

So let's we do this in a different color, so let me pick out the multiples of five.

Double Precision Number

Here's a chart! )

Law of multiple proportions

They are about an order of magnitude longer, about 11 times longer in duration on average, than in a normal child.

light bulb, every numbered light bulb would that is a multiple of three is going to be switched.

Least common multiple

How old are Talia and Jared?

This is clearly 5 times 10, this is 8 times 5, this is the same number again, also 8 times 5, so all of these are multiples of 5, 45, that's a 9 times 5, 3 not a multiple of 5, 25 clearly 5 times 5.

Both 10 and 100 is the least common multiple.

So this is the third piece of rope here.

For really simple problems like this you can use common sense.

Well it's just this plus 1, so it's y the 3 2 power, and then times the inverse of this.

Well, there's 15 coins and 5 of them are fair, so it's 5 out of 15, so it's 1 3.

So we could get any point on this line right there.

So this is how many marbles he had before tripling, and now he's tripling, now he's tripling his marbles.

3 times 4 times 1 2.

If we are going from 3 cups to 9 cups of oatmeal how much more oatmeal we are using? we are using 3 times more , 3 x 3 9

So I circled all the multiples of 5.

Let's figure out the rules...

How do we do that?