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### Course: 6th grade (Eureka Math/EngageNY) > Unit 2

Lesson 4: Topic D: Number theory—thinking logically about multiplicative arithmetic- Divisibility tests for 2, 3, 4, 5, 6, 9, 10
- Recognizing divisibility
- The why of the 3 divisibility rule
- The why of the 9 divisibility rule
- Divisibility tests
- Intro to even and odd numbers
- Greatest common factor examples
- Greatest common factor explained
- Greatest common factor
- Greatest common factor review
- Least common multiple
- Least common multiple: repeating factors
- Least common multiple of three numbers
- Least common multiple
- Least common multiple review
- GCF & LCM word problems
- GCF & LCM word problems

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# Least common multiple: repeating factors

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.

## Want to join the conversation?

- how is the gcf different from the lcm(14 votes)
- 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.(29 votes)

- what is the greatest common factor of 120 and 192(5 votes)
- 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**.(24 votes)

- what is that fancy bracket that Sal draws around the 2*3*5 at1:18called, if it is called anything other than a bracket?(5 votes)
- 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.(9 votes)

- 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?(8 votes)
- What is the prime factoring(4 votes)
- what is the least common multiplies of 144 and 38?(4 votes)
- 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).(5 votes)

- can there be one repeating factor number than two repeating number numbers ?(4 votes)
- What does a whole number with a line over it mean?(3 votes)
- 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}.(2 votes)

- how do u do this(2 votes)
- how would you find the lcd with letters. For example: x/ab;y/bc;z/ac(3 votes)
- 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.(1 vote)

## 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.