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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
