Hi guys, welcome to another class on Gis' channel. And today you will learn how to calculate LMC, least common multiple. Let's go then?
So take the opportunity to subscribe to the Gis Channel, if you're not already subscribed and don't forget to leave a thumbs up for Gis, okay? So let's calculate the MMC, but MMC, what does MMC mean? It means least common multiple, that is, it is the smallest of the common multiples between at least two numbers, right?
So I'm going to explain here to you the two methods of solving it, two methods, the conventional and the practical method, okay? But hey, to do this conventional method that I'm going to explain now, firstly, you need to remember the concept of multiple well, and for that I leave the indication of the class so that you can review these concepts, agreed? So let's do it.
To calculate the multiples of the MMC of 8 and 12, I will write down what are the multiples of 8 and what are the multiples of 12. So look here folks, multiples of 8. Who are the multiples of 8?
You need to study the multiplication tables, if you don't remember the multiples, you can't do it! You have to study the multiplication tables, right? Go to class and go there to study the multiplication tables and get everything right, you'll be a winner here in the MMC part.
So the multiples of 8 are: 0, 8, 16, 24, 32 or 40. . .
But how far do I go? Because multiples are infinite, right? What number do I go to?
People, it will depend, it will depend on the other set of multiples, right? Because you'll have to find which one will be repeated in both sets. So I can't say, go until the fifth number, it's not possible, you'll have to see when it will repeat itself, when it repeats you stop, or if it doesn't happen you continue, so let's do a couple more here, look: 40 , 48, 56 then would come 64, I like to do the multiples, right, thinking about the multiplication tables.
Now let's find out which numbers belong to the number twelve. What are the multiples of 12? So it's going to be 0, 12, 24, you're already looking at something, right?
But shall we continue a little longer? The 36, 48, 60. .
. Do I need to continue guys? I don't need to continue, do I?
Which I'm sure you've already looked at and said, Gis, stop, like that game of stop, stop, right? So, I'm going to put the indication here with the three dots, because I know that the multiples are infinite, right? Very well, now tell me, of these multiples of 8 and these multiples of 12, which numbers were repeated?
So they're repeating themselves, which we call common multiple, MC I'll put it, common multiple, okay? So the common multiples are 0, who else did you repeat? The 24, common people, is because they are in both sets at the same time, that's why it is common, common multiple.
That's why I put MC, and you won't think it's MC who sings the songs there, right? It's MC of common multiple, ok? 0, 24 the next thing that was repeated was 48 after which it would continue to repeat itself.
But I need to know which ones keep repeating themselves? No, why? Because when I'm calculating the MMC, I want the smallest, the smallest multiple that is common.
Of these common multiples here, we never put 0, right people, otherwise 0 would be everyone's MMC. So the 0 will be excluded, it cannot be anyone's MMC. So what will be the MMC between 8 and 12?
Which of these common multiples here is the smallest of them? In other words, the first one that appeared, you don't even need to do anything else, it's number 24. Okay, this is the MMC.
Now stop and think about the multiplication table, I didn't even need to write everything I wrote. In the 8 times table and the 12 times table, what is the first number that is repeated? So you had to be good at multiplication tables, think quickly and which one is first?
It's 24, so 24 is the result of the MMC between 8 and 12. So, it's as simple as what I did, it's the conventional method, then we have the practical process guys, which will be like this, you're going to write then the numbers you want here, which in this case I want MMC between 8 and 12, and you will pass a vertical bar like this. To carry out this practical process you need to know the prime numbers, so I also leave instructions for you to remember the concepts of prime numbers, okay?
Because here we always decompose prime numbers, take advantage and watch the decomposition class too, ok? So let's go! First prime number that divides at least one of the two is 2, so here it is 8 by two are 4, 12 by 2 of the 6, it's like if I did the division, right, I did the risk of division here, I did it, I didn't do it, I do that, right, but It's a different way 8 / 2 I'll put the result below, okay?
Then 12 / 2 puts the result below. And now? What is the prime number that divides at least one of them there?
I'm still with 2, right, because they are even, so it's 2, if I divide it by 2 it will be 2 and 6 / 2 will be 3, now what? What is the prime number that divides at least one of them? Continue with 2, but what if I wanted to do 3 first, could I?
It could, it won't change the final result, but I like to do it in order, okay? Now here is 1 and 3 divided by 2, 3 divided by 2 gives 1 and a half, I can't use a broken number, right, a decimal number is just a whole number that we work with here. So I lower the 3, and now who gives?
It is the number 3 itself that gives 1 and that gives 1. But what then? I already did it.
How will I get the result? Now you come here and you multiply these numbers that we made here, which will give you how much 2 x 2 are 4 and 2 are 8 x 3 are 24. So what?
Then the MMC result = 24. Did you see the two ways of becoming people? Conventional process , conventional method, and the practical process, this one is much faster, that's why it's called practical process.
But for you to do this here, before learning this here, before doing this here, you have to know what prime numbers are, if you don't know prime numbers you can't do it for this one. That's why teachers teach MMC starting with the process, with the conventional method, which is the part of calculating the multiples, which makes perfect sense, right, MMC least common multiple, right? So that's why you learn this first, and then learn this one, okay?
You learned the concept, then you go to the practical method and nail it, ok? Shall we do more examples then? But now I'm going to do it the practical method, ok?
Let's go then? People, I said that I would do it just for the practical process, right? They scolded me here, they said that it was to do another case showing the conventional process here.
So see that I already wrote down for you what the multiples are, okay? Now what is the MMC between 9 and 15 and 18. So I already wrote here what are the multiples of 9, the multiples of 15 and the multiples of 18, right?
I already made the list here for you, now it's up to you to check these three, now I put the MMC with three, that first example there we did between 8 and 12, it was two numbers and now I brought it with three numbers, now, is it the same way? in the same way, but now I'm going to have to look at which number is common to all three sets at the same time, okay? So we already know that 0 is , which is repeated, so we can now put it here, Mc, Mc of common multiples, okay?
So come on, who are Mc? It's the zero that we already know is repeated, but it won't be him, I don't even know why I wrote it, right, what else now? Do you already see it?
I'm sure you 're going to say which one? which? which?
But look, if I say 60, is 60 people? No, right, because 60 is only in this table and not in this table. Let me see another one here, 18 people, 18 is here and there is here, could it be 18?
No, I said that to be a common multiple it has to be present in all three sets here since I have three sets of multiples. Have you ever found what number is in the three sets of multiples? I'm winding you up, right?
So we have here, the number 90 which is in the three sets of multiples, right? So 90, and then I need to find who's next here, folks? No, right, because when I do MMC, apart from 0, removing 0, it is the first number that appears.
So I already know that the MMC is between 9 between 15 and 18, the MMC is 90 there, see how difficult it is, you have to study the multiplication tables well here, because you can see that the multiplication table, right, there are people who think that the multiplication table goes up to 10. Of course not, the multiplication table is a multiplication, isn't it? I can find the multiples, the 15 the multiples of 18 and how much I need right?
And now let's do the practical process now? Now you trained with three numbers, look here, so first thing I'm going to write a prime number here in this row, we're just going to go prime number, okay? A prime number that divides at least one of them, I'm sure you said, will start with 3, right?
There is, A lot of people like to start with 3, since these three numbers are in the 3 times table, but I'm going to start with 2, just because I like number 2, there's no way to stay in order. Starting with 2, 9 / 2 does not give below 9, ok? 15 / 2 does not give an exact division below 15.
18 divided by 2 from 9, ok? Now who do I put again, 2? No, right, because here you can't divide any of them by 2, so now the next prime number that works is 3, and you could have put 5, because I 15 can be divided by 5, but in order, right?
Now making the order, 9 for 3 of 3. 15 / 3 of 5 and 9 for 3, 3 cool, okay? Now continuing with 3 again 3 by 3 with 1, below 5, and here we get 1.
And now for us to finish, what number divides 5? It's 5 itself since it's a prime number, so 1 becomes, becomes 1, and becomes 1. Now to find the result of this MMC, I'm going to multiply these terms that I found here, these factors, right?
2 times 3 = 6, 6 x 3 = 18 and 18 times 5 Hey, are you in doubt? Look, huh, I see that you're in doubt, 40 goes 4, 5 x 5= 49, 90 people. Look how wonderful, look how quickly I did this, so I don't need to make this whole list here of the numbers in the set of multiples of these numbers, right?
It's no longer easy to do it through the practical process, so I hope you understood and enjoyed Gis' explanation. Take advantage and subscribe to the channel? Not yet?
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goodbye. . .
