how is the gcf different from the lcm

The gcf is the LARGEST number that WILL DIVIDE INTO both given numbers. As such, it will be less than at least one (usually both) of the given numbers. The lcm is the SMALLEST number that BOTH GIVEN NUMBERS DIVIDE into. As such, it will be greater than at least one (often both) of the given numbers.

what is the greatest common factor of 120 and 192

First, let's list out the *factor pairs* of each number. ``` 120: 1 and 120; 2 and 60; 3 and 40; 4 and 30; 5 and 24; 6 and 20; 8 and 15; 10 and 12 192: 1 and 192; 2 and 96; 3 and 64; 4 and 48; 6 and 32; 8 and 24; 12 and 16 ``` Next, let's order the factors of each number from *least to greatest*. ``` 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24 30, 40, 60, 120 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192 ``` Based on these two lists, let's make a list of *all* of the common factors of 120 and 192. `120 and 192: 1, 2, 3, 4, 6, 8, 12, 24` The GCF of 120 and 192 is the greatest value in this list, which is *24*.

what is that fancy bracket that Sal draws around the 2*3*5 at 1:18 called, if it is called anything other than a bracket?

A bracket is [ or ] . A brace is { or } . I guess you can call it a squiggly line that connects the selected objects and relates them to something else in the part that sticks out in the middle.

what is the least common multiplies of 144 and 38?

144 = 12*12=3*2*2*3*2*2 38=2*19, so since they only have a 2 in common, multiply 144*19 to get the LCM (the 2 in 38 will not repeat).

What is the prime factoring

https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-prime-factorization-prealg/v/prime-factorization

how would you find the lcd with letters. For example: x/ab;y/bc;z/ac

The denominators use 3 unique factors: a, b and c. None of them occur more than once in any fraction. So, your LCD = abc. Hope this helps.

What does a whole number with a line over it mean?

I've never seen that notation. But here are some possible meanings: (1) Someone didn't write a repeating decimal correctly. 6.666666 should be written as 6.6 with a bar or the .6 portion. (2) Someone forgot to write the top portion of a fraction. (3) I've read that it can be a VERY rarely used way of indicating "average". So a 3 with a line over it would indicate that 3 is the average of the data set {1,2,3,4,5}.

factor first two 18 is 3*3*2 and 24 is 3*2*2*2, so these have a 3 and 2 in common, LCM is 3*3*2*2*2 or 9*8 (which is also 18*4 - the first times what is left in the second) 72. With 72 being 3*3*2*2*2. 60 is 5*3*3*2, so have two 3s and a 2 in common, answer would be 3*3*2*2*2*5 or 72*5=360. 360/18 = 20 (2*2*5). 360/24 = 15 (3*5), and 360/60 = 6 (3*2) which shows that all three do not have a common factor. Thus answer is 360.

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Class 6 (Old)

Course: Class 6 (Old) > Unit 3

Lesson 8: Lowest common multiple

Least common multiple: repeating factors

Name: Least common multiple: repeating factors
Uploaded: 2013-07-25T00:52:39Z
Description: To find the Least Common Multiple (LCM) of two integers, follow these steps: 1) Find the prime factorization of both numbers. 2) Determine which prime factors are needed for the least common multiple (LCM) to be divisible by both numbers. 3) Multiply the necessary prime factors together to get the least common multiple (LCM).

Google Classroom

To find the Least Common Multiple (LCM) of two integers, follow these steps: 1) Find the prime factorization of both numbers. 2) Determine which prime factors are needed for the least common multiple (LCM) to be divisible by both numbers. 3) Multiply the necessary prime factors together to get the least common multiple (LCM). Created by Sal Khan.

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ja'cara.webb.05
Posted 7 years ago. Direct link to ja'cara.webb.05's post “how is the gcf different ...”
how is the gcf different from the lcm
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(15 votes)
Answer
- Judith Gibson
  Posted 7 years ago. Direct link to Judith Gibson's post “The gcf is the LARGEST nu...”
  The gcf is the LARGEST number that WILL DIVIDE INTO both given numbers.
  As such, it will be less than at least one (usually both) of the given numbers.
  The lcm is the SMALLEST number that BOTH GIVEN NUMBERS DIVIDE into.
  As such, it will be greater than at least one (often both) of the given numbers.
  Comment on Judith Gibson's post “The gcf is the LARGEST nu...”
  (27 votes)
Vaishavi Arulla
Posted 5 years ago. Direct link to Vaishavi Arulla's post “what is the greatest comm...”
what is the greatest common factor of 120 and 192
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(7 votes)
Answer
- Danny
  Posted 5 years ago. Direct link to Danny's post “First, let's list out the...”
  First, let's list out the factor pairs of each number.
  120: 1 and 120; 2 and 60; 3 and 40; 4 and 30; 5 and 24; 6 and 20; 8 and 15; 10 and 12 192: 1 and 192; 2 and 96; 3 and 64; 4 and 48; 6 and 32; 8 and 24; 12 and 16
  
  Next, let's order the factors of each number from least to greatest.
  120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24 30, 40, 60, 120 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
  
  Based on these two lists, let's make a list of all of the common factors of 120 and 192.
  120 and 192: 1, 2, 3, 4, 6, 8, 12, 24
  The GCF of 120 and 192 is the greatest value in this list, which is 24.
  Comment on Danny's post “First, let's list out the...”
  (23 votes)
mem
Posted 8 years ago. Direct link to mem's post “what is that fancy bracke...”
what is that fancy bracket that Sal draws around the 2*3*5 at
1:18
called, if it is called anything other than a bracket?
Button navigates to signup pageComment on mem's post “what is that fancy bracke...”
(6 votes)
Answer
- skyfall17
  Posted 8 years ago. Direct link to skyfall17's post “A bracket is [ or ] . A b...”
  A bracket is [ or ] . A brace is { or } . I guess you can call it a squiggly line that connects the selected objects and relates them to something else in the part that sticks out in the middle.
  Comment on skyfall17's post “A bracket is [ or ] . A b...”
  (10 votes)
21hannahsireginald
Posted 7 years ago. Direct link to 21hannahsireginald's post “when i watched the video,...”
when i watched the video, i got confused because i keep trying to do it but i keep getting the answers wrong can you help me more?
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(8 votes)
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inalaska73
Posted 7 years ago. Direct link to inalaska73's post “What is the prime factori...”
What is the prime factoring
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(4 votes)
Answer
- KathyC
  Posted 7 years ago. Direct link to KathyC's post “https://www.khanacademy.o...”
  https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-prime-factorization-prealg/v/prime-factorization
  Comment on KathyC's post “https://www.khanacademy.o...”
  (8 votes)
afritz
Posted 4 years ago. Direct link to afritz's post “what is the least common ...”
what is the least common multiplies of 144 and 38?
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(5 votes)
Answer
- David Severin
  Posted 4 years ago. Direct link to David Severin's post “144 = 12*12=3*2*2*3*2*2 3...”
  144 = 12*12=3*2*2*3*2*2
  38=2*19, so since they only have a 2 in common, multiply 144*19 to get the LCM (the 2 in 38 will not repeat).
  Button navigates to signup page
  (6 votes)
Carolyn Logan
Posted 5 years ago. Direct link to Carolyn Logan's post “how would you find the lc...”
how would you find the lcd with letters. For example: x/ab;y/bc;z/ac
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Kim Seidel
  Posted 5 years ago. Direct link to Kim Seidel's post “The denominators use 3 un...”
  The denominators use 3 unique factors: a, b and c. None of them occur more than once in any fraction. So, your LCD = abc.
  
  Hope this helps.
  Button navigates to signup page
  (2 votes)
Cheryl Jones
Posted 7 years ago. Direct link to Cheryl Jones's post “What does a whole number ...”
What does a whole number with a line over it mean?
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(4 votes)
Answer
- KathyC
  Posted 7 years ago. Direct link to KathyC's post “I've never seen that nota...”
  I've never seen that notation. But here are some possible meanings:
  (1) Someone didn't write a repeating decimal correctly. 6.666666 should be written as 6.6 with a bar or the .6 portion.
  (2) Someone forgot to write the top portion of a fraction.
  (3) I've read that it can be a VERY rarely used way of indicating "average". So a 3 with a line over it would indicate that 3 is the average of the data set {1,2,3,4,5}.
  Button navigates to signup page
  (2 votes)
CASSIE Calhoun-liebnow :D
Posted 6 years ago. Direct link to CASSIE Calhoun-liebnow :D's post “Lcm (18, 24, 60)”
Lcm (18, 24, 60)
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(4 votes)
Answer
- David Severin
  Posted 6 years ago. Direct link to David Severin's post “factor first two 18 is 3*...”
  factor first two
  18 is 3*3*2 and 24 is 3*2*2*2, so these have a 3 and 2 in common, LCM is 3*3*2*2*2 or 9*8 (which is also 18*4 - the first times what is left in the second) 72.
  With 72 being 3*3*2*2*2. 60 is 5*3*3*2, so have two 3s and a 2 in common, answer would be 3*3*2*2*2*5 or 72*5=360. 360/18 = 20 (2*2*5). 360/24 = 15 (3*5), and 360/60 = 6 (3*2) which shows that all three do not have a common factor. Thus answer is 360.
  Button navigates to signup page
  (2 votes)
bryant pablo
Posted 8 years ago. Direct link to bryant pablo's post “can there be one repeatin...”
can there be one repeating factor number than two repeating number numbers ?
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(4 votes)
Answer

Video transcript

We need to figure out the least common multiple of 30 and 25. So let's get our little scratch pad out here. And we care about 30 and we care about 25. And I'm going to do this using the prime factorization method which I just like more. Let's find the prime factorization of both of these numbers. So 30, it's divisible by 2. It's 2 times 15. 15 is 3 times 5. And now we've expressed 30 as the product of only prime numbers, 2 times 3 times 5. Now let's do the same thing for 25. 25 is-- well that's just 5 times 5. So let me write that down. 25 is equal to 5 times 5. Now to find the least common multiple, let me write this down, the least common multiple of 30 and 25 is going to have a number whose prime factorization is a super set of both of these or has all of these numbers in them as many times as we have in any one of these. So it's the least common multiple. Well it has to be divisible by 30. So it's going to need a 2 times a 3 times a 5. This is what makes it divisible by 30. But it needs to also be divisible by 25. And in order to be divisible by 25, you need to have two 5s in your prime factorization. Right now our prime factorization only has one 5. So let's throw. So we have one 5 right over here. We need another 5. So let's throw another 5 right over here. So now this thing clearly has a 25 in it. It's clearly divisible by 25. And this is the least common multiple. I could have, if we just wanted a common multiple, we could have thrown more factors here and it would have definitely been divisible by 30 or 25, but this has the bare minimum of prime factors necessary to be divisible by 30 and 25. If I got rid of any one of these, I wouldn't be divisible by both anymore. If I got rid of this 2, I wouldn't be divisible by 30 anymore. If I got rid of one of the 5s, I wouldn't be divisible by 25 anymore. So let's just multiply it out. This is essentially the prime factorization of our least common multiple. And this is equal to 2 times 3 is 6, 6 times 5 is 30, 30 times 5 is equal to 150. And of course, we can check our answer, 150. Check it, and we got it right.