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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
