[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Find the least common multiple of
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,15x, 20, and x squared plus 5x.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So when you're trying to find
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,the least common multiple of
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,a bunch of numbers you wanna
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,break them down into their
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,smallest constiguent parts.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And if you're dealing with regular
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,numbers, those smallest
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,constiguent parts are the
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,prime factorization numbers.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And if you're dealing with
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,things that have variable expressions
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,you just wanna factor them into
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,their simplest possible components.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,You can't really call
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,those prime factorizations.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So let's try to do it.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And once you do that,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,the least common multiple
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,just needs to be the
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,smallest number that can be
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,factored into those constiguents
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,and those constiguents in them.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So let's factor each of them.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So if I factor 15x,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,this is the same things as
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,15 times x and 15
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,is three times five.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Both three and five are prime.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So we can factor this as
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,3 times 5 times x.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,That's the, well, for the
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,coefficient we've done the
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,prime factorization.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And then x,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,that's as much as we can factor
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we don't know if x
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,is prime or not.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It's a variable.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Let's do the same thing for 20.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So 20 here
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,can be factored into
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,2 and 10.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And 10 can be factored
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,into 2 and 5.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So 20 is equal to 2 times
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,2 times 5.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And that's just a straight factorisation
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Now let's do x square plus 5x
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,x squared plus 5x, we can factor out
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,and x, both of these terms are divisible by x
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,so this is equal to x times x plus 5
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Right, if you divide... if you factor out an x here
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,you just get an x, if you factor out a x
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,out of 5x, you just get a 5.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And so the least common multiple, so let me write it down,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,the least common multiple has to have the smallest number that has all of these components
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,at least, so it has all of these factors in it.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So let's just start with the smallest numbers and then we'll get to the variables.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So it has to have at least to 2s, because we have two 2s here,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,we don't have any of them here, we have to have at least two 2s.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So we have two, let me do one of those pink 2s,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,so it has to have at least two 2s,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,two times two, two times two.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,If it's going to be divisible by 20, it's also gonna need a 5,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,but we'll get to that in a second.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So we have to have at least two 2s, and then it needs to have at least one three,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,it needs at least one three, if it has any chance of being divisible by 15x.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So it has to have at least one 3, none of these guys,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,so at least one 3, and then 5
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,if it has any chance of being divisible by 15x, it has to have
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,at least one 5, if it has any chance of being divisible by 20,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,it has to have at least one 5, so it has to have at least one 5.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This one 5 right over here, will help make it sure that it is divisible
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,both by 15x and 20, although we haven't put all of the factors there.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Although this is already divisible by 20, because we have the 2 times 2 times 5 here
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This isn't quite divisible by 15x yet,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,because we don't have an x here.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It is divisible already by 15,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,because we already have the 3 times 5.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And then you get to the x. This right over here has one x value,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,so in order to be divisible by 15x, it has to have at least one x here
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And so this is already divisible by 15x, you have 15x right over here
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,3 times 5 times x
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It's already divisible by 20
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,you have 2 times 2 times 5, that is 20.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Is it divisible by x square + 5x?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Well it does have this x here,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,but it still doesn't have an x plus 5 in it.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It still doesn't have and x plus 5,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,so let me do that in orange.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So this, the least common multiple also needs,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,an x plus 5 over here.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And so this is the least common multiple.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,If you wanna multiply it out, to may be simplify it a little bit,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,2 times 2 is 4, 4 times 3 is 12, 12 times 5 is 60,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,60 times x is 60x,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,so this is 60x
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,60x times x plus 5.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And if we want we can multiply it out.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,60x times x plus 5 is
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,60x squared plus, 60 times 5 is 300, 300x
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And there you go, the least common multiple.