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welcome to math with mr j

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in this video i'm going to cover least

common multiple also known as lcm least

common multiples are commonly used when

working with fractions as well as other

types of math problems so least common

multiples show up in a variety of

situations now when we're talking about

least common multiples let's break that

down and think about what this means

well least means the smallest in value

common in this case means that something

is being shared and then multiple well

we get a multiple of a number when we

multiply that given number by an integer

think multiply or skip count when you

think of multiples now that may sound a

little confusing but it's actually not

too bad i think an example will make it

much more clear so let's jump into

number one where we have three and six

let's start with some multiples of three

and remember think multiply or skip

count so let's

write the first five multiples of three

and then we'll go from there so three

times one is three

three times two is six

three times three is nine

three times four is twelve three times

five is 15. so i'll stop there and then

we'll write some multiples of 6 and see

if we have any in common and if we do

we're going to look for the least that

they have in common now those multiples

go on forever so i suggest writing four

or five multiples for each given number

see if you have any in common and then

go from there you can always extend your

lists of multiples so let's write some

multiples of six

so again think multiply or skip count so

6 times 1 is 6 6 times 2 is 12

times 3 is 18

times 4 is 24

and then times 5 is 30. so

we did 5 multiples for each let's see if

we have any

common multiples so

we have 12 in common

and we also have 6

in common

but we want the least so 6 is going to

be the least common multiple between 3

and 6. so i'll put lcm

which stands for least common multiple

equals

six

let's try another example and move on to

number two where we have four and ten so

we'll start with some multiples of four

so skip count or think of it as 4 times

1 4 times 2 so on and so forth let's

skip count for this one so 4

8

12

16 20. so we'll write 5 for that one

let's do 10 now

10

20

and you may notice that we have

something in common there and that's

going to be the least common multiple if

you notice that you have a least common

multiple there's no need to keep writing

out multiples we have our answer

so 20 is going to be our least common

multiple so least

common multiple

equals

20.

let's move on to number three where we

have nine and six so we'll start with

some multiples of nine here so 9

18

27

36

45

and now some multiples of 6

6

12

18

and we have our least common multiple

right here which is going to be 18 so

our lcm

equals

18.

now i do want to mention before moving

on to number four that for these

problems we're going to have an infinite

amount of common multiples since we have

an infinite amount of multiples we're

therefore going to have an infinite

amount of common multiples we can always

extend our lists further in order to

find more common multiples but since we

want the least we need to focus on at

least and once we have that least common

multiple we have our answer

let's move on to number four where we

have 12 4 and 8 so we have three numbers

and we need to find the least common

multiple between all three

let's start with some multiples of 12.

so 12

24

36

48

and

60.

let's do four now so

four

eight

twelve

sixteen

and twenty

and lastly

eight

so 8

16

24

32

and 40.

so as we look at these lists we do have

some common multiples but we don't have

any common multiples between all three

and we need a common multiple between

all three and specifically the least

common multiple

so what we can do we can extend our

lists until we find that least common

multiple now the 12s the multiples of 12

we're already at 60. so let's leave that

list let's look at the 4. we're only at

20 there so let's extend the lists of

multiples for four so our next multiple

is going to be 24 and that's going to be

our least common multiple

24

24

and 24. so if you don't see a least

common multiple you can always extend

your lists until you find it so for

number four our lcm

equals 24.

so there you have it there's how you

find the least common multiple i hope

that helped thanks so much for watching

until next time

peace