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GenX-Education
  • 7/28/2024
Transcript
00:00Hi kids, today we will learn how to find out the LCM of two or more numbers with method
00:09which is called prime factorization.
00:13So let's get started.
00:16LCM means lowest common multiple.
00:21First of all, let's see what is a multiple of a number.
00:27We have a number 5, what are its multiples?
00:33Numbers obtained by multiplying 5 with any number are its multiples.
00:41Here all, 0, 5, 10, 15, 20, 25, 30 and so on, all the numbers that comes in a multiplication
00:54table of 5 or step counting by 5 are its multiples.
01:01Remember, 0 is a multiple of every number as multiple of a number is any number which
01:09we get on multiplying it with any number and we get 0 when any number is multiplied with
01:180.
01:202 multiplied by 0 equals 0.
01:25So, 0 is a multiple of 2.
01:283 multiplied by 0 equals 0.
01:33So 0 is a multiple of 3.
01:3512 multiplied by 0 equals 0.
01:40So 0 is a multiple of 12.
01:43So, 0 is a multiple of every number.
01:48Now, here we have another number, 7.
01:53Let's list its multiples.
01:57We now know multiples of a number are all numbers that comes in its step counting or
02:04its multiple.
02:06So multiples of 7 are 0, 7, 14, 21, 35, 42, 49, 56, 63, 70, and so on.
02:21Now let's learn how to find LCM or least common multiple of 6 and 8 using a method
02:29that uses prime factorization.
02:32So let's learn it.
02:35We have to find the LCM of 6, 8.
02:40So we will do the prime factorization of 6 and 8 first.
02:45We divide all the numbers with prime numbers only.
02:50That is 2, 3, 5, 7, starting with the smallest prime number, that is 2.
02:59And keep dividing till every number is reduced to 1.
03:03So let's start, 6 divided by 2 equals 3, so write 3, put a comma.
03:12Now 8 divided by 2 is 4, so now write 4.
03:20Now again, we have to try dividing the resulting numbers by smallest prime number, that is
03:262.
03:27If any number cannot be divided by 2, write it as it is.
03:33So write 3, as it is, put a comma.
03:37Now 4 divided by 2 equals 2, so write 2.
03:44Now again, try dividing the numbers by 2.
03:48Again, 3 cannot be divided, write it as it is, 2 divided by 2 equals 1, write 1 here.
04:00Now only one number, that is 3, is left.
04:03It cannot be divided by 2, so take next smallest prime number, which is 3.
04:10Now 3 divided by 3 equals 1, write 1, put comma, and bring down 1.
04:19Now every number is reduced to 1, and we used only prime numbers.
04:25Now the next step is, take all these numbers, which we used to divide the numbers, and
04:30multiply them.
04:32So 24 is the LCM of 6 and 8.
04:39Now let's take another example.
04:42We have to find the LCM of 4, 12, 9, 30.
04:49So first we do the prime factorization of these numbers.
04:53First write the numbers like this.
04:56Now take the smallest prime number, that is 2.
05:004 divided by 2 equals 2.
05:049 cannot be divided, so write it as it is.
05:1012 divided by 2 equals 6, so write 6.
05:1530 divided by 2 equals 15, write 15.
05:21Now again, take 2.
05:242 divided by 2 equals 1, 9 cannot be divided, so write it as it is.
05:326 divided by 2 equals 3, 15 cannot be divided, so write it as it is.
05:42Now we cannot take 2, as not even a single number can be divided by 2, so take the next
05:49prime number, that is 3.
05:52If there is 1, simply write it as it is.
05:579 divided by 3 equals 3.
06:013 divided by 3 equals 1.
06:0515 divided by 3 equals 5.
06:10Now again, take 3, as one number is there, which can be divided by 3.
06:19Now we can't take 3, as no number can be divided by 3.
06:24Now next prime number is 5, yet 5 will divide the number left.
06:30All numbers reduce to 1 now.
06:34Now next step is take all these numbers and multiply.
06:39180 is the least common multiple, LCM of 4, 9, 12, and 30.
06:49So kids, this method is easier and shorter to find LCM, when you have more numbers or
06:57bigger numbers.
06:58Okay kids, now you may go ahead and take a quiz to learn more.
07:03Bye bye.