WEBVTT mathematics/basic-math/pyo
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This next lesson is on finding the least common multiple.
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To review, a multiple is a number or the numbers that the original number can multiply into.
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If I have a number 4, the multiples would be 4, 8, 12, 16, 20, and so on.
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Multiples would be numbers that the original number can multiply into.
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The least common multiple is known as the LCM; we are comparing two numbers.
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From the multiples of the two numbers, we are going to find the smallest common multiple.
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In order to do this, there is two methods that we can use.
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The first method is to simply list out the multiples of each number.
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You are going to find the smallest one.
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For 6, the multiples would be 6, 12, 18, 24, 30, 36, 42, 48.
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I am going to just stop there for now.
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List out the multiples of 10; for 10, 20, 30, 40, 50, and 60.
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If you look at this, from these numbers, a common multiple is 30.
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If I were to keep going, for the 6, this would be 54 and 60.
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Another common multiple would be 60.
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But again I want to find the least common multiple.
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It is going to be the smallest common multiple which is 30.
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The LCM of 6 and 10 would be 30.
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Another method to finding the LCM is going to involve prime factorization.
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If you don't remember prime factorization, you can go back to that lesson and just review over that.
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I am going to find all the prime factors of 6 and 10.
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To do that, I have to use a factor tree.
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6, I am going to break down into 3 and 2.
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Circle them because they are prime numbers.
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10, the factor pairs of 10 would be 5... 5 is a factor... and 2.
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That is also prime; I circle it.
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Look at the prime factors of 6, 3 and 2.
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I look at the prime factors of 10 which is 5 and 2.
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I look for any common factors; the common factor between 6 and 10 is 2.
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If I list this out, 6 is 3 and 2.
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The prime factors of 10, 5 and 2; they have a common factor of 2.
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When they have a common factor, I am going to take one of them and cross it out.
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Cross out only one of them.
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Then I take all the remaining numbers--3, 5, and then this 2.
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I am going to multiply them out.
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The LCM is going to be 3 times 5 times 2 which is equal to 30.
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Whichever method you would like to use, you will still get the same answer of 30.
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Let's find the LCM of 12 and 15; you can pause it.
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I want you to try to use both methods to find the LCM.
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Then just come back and we will go over it.
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12 and 15; I am going to use the second method for all these examples.
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I am going to use the factor tree method to find all the prime factors of these numbers.
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For 12, I can use a factor pair of 6 and 2.
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Or I can use 4 and 3.
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3 is a prime number; I am going to circle it.
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4, I am going to break up into two prime numbers, 2 and 2.
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I circle those numbers.
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For 15, the factor pair would be 5 and 3.
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These are both prime numbers; I am going to circle them.
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For 12, all the prime numbers would be 2 times 2 times 3.
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The prime factorization of 15 is 5 and 3.
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I look for any common numbers between 12 and 15.
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They have a common number of 3.
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I am just going to take one of them and cross it out.
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These are common; there is a 2 here and a 2 here.
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But that is within the same number, 12.
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I don't want to cancel that out.
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It has to be one from here and one from the other number.
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I am going to take the remaining numbers--2, 2, 5, and 3.
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I am going to multiply them out.
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My LCM is going to be 2 times 2 times 5 times 3.
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This is going to be 4; this is going to be 15.
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My answer is 60.
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The next example is finding the LCM of 16 and 20.
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Let's use the factor tree; the factor pair of 16 would be 4 and 4.
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You can also use 8 and 2; circle them because they are prime.
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2 and 2, circle those numbers.
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For 20, I can use 10 and 2; or I can use 5 and 4.
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5 is a prime number; I am going to circle that one.
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4 becomes 2 and 2; circle those.
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For 16, the prime factorization would be 2 times 2 times 2 times 2.
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For 20, 5 times 2 times 2.
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Look at this; we have a common number here.
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I am going to cancel one of these out; it doesn't matter which one.
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That took care of that pair.
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We have a 2 here and another 2 here, another common number.
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Again I am going to cancel out one of them.
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I am going to leave the other one.
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You are going to take all the remaining numbers--2, this 2, 5, 2, including this one, 2.
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I am going to multiply them all out.
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The LCM is going to be 2 times 2 times 5 times 2 times 2.
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This is 2 times 2; this is 4; times 10 times 2.
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You are going to get 80 as your answer.
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Example three, let's use 15 and 25.
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The prime factors of 15, 5 and 3; for 25, we have 5 and 5.
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I can write them out; then for 25.
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They have a common number of 5.
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I am going to cancel out one of those factors.
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Even though I have a 5 here and a 5 here,
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I am not going to cancel that out because they are both in the same number, 25.
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I take the remaining numbers.
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My LCM is going to be the product of those numbers.
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3 times 5 times 5; my answer is going to be 75.
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For this example of 12 and 18, we are going to find the LCM, the least common multiple.
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In order to do that, I am going to use the factor tree method
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to find all the prime factors which is the second method that we went over.
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12, I am going to use the factor pair 4 and 3.
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I can also use 6 and 2.
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This is a prime number; I am going to circle this.
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For 4, break this up into 2 and 2.
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They are both prime; I am going to circle them.
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Then do the same thing for 18.
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For 18, I can use 9 and 2; or I can use 6 and 3.
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This is a prime number; circle that one.
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For 6, I am going to use 2 and 3.
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Circle them because they are prime.
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For 12, all the prime factors are going to be 2, 2, and 3.
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For 18, 2 times 3 times another 3.
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I am going to look for any common factors between 12 and 18.
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I know that there is a common factor of 3 for both 12 and 18.
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I am going to take one of the numbers and just cross it out.
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Just cancel one of the numbers out.
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I also have a common factor of 2; 2 and 2.
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I am going to take that and cancel one of those out.
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Even though I have a 2 here and a 2 here, they are within the same numbers.
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I am not going to cancel that out.
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I take all the remaining numbers--this one, this one, and these two.
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I am going to multiply them out to find the least common multiple.
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It is going to be 2 times 2 times 3 times 3.
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I am going to get 4 times 9 which is going to be 36.
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The least common multiple of 12 and 18 is 36.
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