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welcome to math with Mr Jay

[Music]

in this video I'm going to cover how to

find the least common multiple also

known as the LCM using prime

factorization now I like using this

strategy and find it helpful when

working with numbers that are a little

larger in value and not as simple to

work with for example the strategy of

listing out multiples of numbers in

order to find the LCM can be kind of

difficult and time consuming when

working with larger numbers in value so

this is a different approach a different

strategy to be familiar with when it

comes to finding the least common

multiple let's jump into our examples

starting with number one where we have

15 and 27. let's start with the prime

factorization of 15 and we will start

with the factors of 3

and five now three is prime so we are

done there

and 5 is prime so we are done there as

well and that's the prime factorization

of 15. we can't break that down any

further now we have

the prime factorization of 27.

let's start with the factors of 3

and 9 3 times 9 equals twenty-seven so 3

and 9 are factors of 27.

3 is prime so we are done there but we

can break 9 down 3 times 3

equals nine

so three is a factor of nine

three is prime so we are done there

and there and that's the prime

factorization of 27. we can't break that

down any further

now we're ready to move to the next step

so we need to list the prime factors of

15 and 27 and match them vertically

let's see what this looks like starting

with

15. so our prime factors from the prime

factorization are three and five or

three times five now four

27 so we have three

times three

times three and you'll notice that big

gap underneath the 5 there we are

matching numbers vertically 27 does not

have a prime factor of five so I left

that blank underneath the 5. now that we

have our prime factors listed and

matched vertically we move on to the

next step where we bring down and I like

to draw a line underneath here in order

to separate these steps so this is a

column

and although we have two threes here

this is a column of Threes so we just

bring

one down we have a three to represent

that column of two threes

times we have a column of five here

times we have a three here

times

another three here

so we end up with three times five times

three times three and by multiplying

these we get our least common multiple

so three times five is fifteen times

three is forty-five times three is one

hundred thirty-five and that's our least

common multiple

so the LCM the least common multiple of

15 and 27

is

135. let's move on to number two where

we have 28 and 52. let's start with the

prime factorization

of 28. now 2 times 14 equals 28 so let's

start with those factors 2 is prime so

we are done there 14 we can break down

two times seven equals 14. so 2 and 7

are factors of 14.

2 is prime so we are done there

and 7 is prime as well so we are done

there and that's the prime factorization

of 28. we can't break that down any

further

now we need the prime factorization of

52. let's start with the factors of 2

and 26 2 times 26 equals 52. so 2 and 26

are factors of 52.

2 is prime so we are done there 26 we

can break that down

2 times 13 equals 26. so 2 and 13 are

factors of 26.

2 is prime so we are done there

and 13 is prime as well so we are done

there and that's the prime factorization

of 52. we can't break that down any

further now we need to list the prime

factors and match them vertically for 28

we have

two

times two

times seven

452

we have two

times two

times

13.

now we need to bring down so we have a

column

of twos here so let's bring down a 2 to

represent that column

times

another column of twos so let's bring

another two down

times

7

times

13.

so we have 2 times 2 times 7 times 13 to

get our least common multiple we have 2

times 2 which is 4 times 7 is 28 times

13. well I'm not sure what 28 times 13

is so let's come to the side here

and multiply 28 times 13. we will start

with 3 times 8

which is 24 3 times 2 is 6 Plus 2.

is 8. we are done here and done here

we need a zero now we have one times

eight

which is eight and then one times two

is two let's add

four plus zero is four eight plus eight

is 16 and then 1 plus 2

is 3. so we get

364. so the least common multiple of 28

and 52. let me squeeze this in here is

300

60

4. so there you have it there's how to

find the least common multiple using

prime factorization I hope that helped

thanks so much for watching

until next time

peace