Common Factors and Common Multiples Video Lecture | Advance Learner Course: Mathematics (Maths) Class 5

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exam now that we have learned so much
about factors multiples and divisibility
we will talk about something very
interesting that is common factors and
multiples then you might be thinking
what what does that mean
common factors and multiples so these
are basically those numbers with same
factors or same multiples so it do you
think that two numbers can have the same
multiple yes of course they can have now
let's do one thing let us try to find
the common multiples of numbers 2 & 3 so
for that we will first write down the
multiples of 2 here and we will write
down the multiples of 3 here so let's do
this exercise so what do we get this
would be 2 4 6 8 then now we will write
considerable number of multiples so that
it becomes easier for us to find out the
common multiples between 2 & 3 so these
are the multiples of 2 now let us write
multiples of 3 so that would be
something like this so now when you look
at the multiples of 2 and multiples of 3
so do you find that there are certain
multiples there are certain numbers
which are multiples of 2 as well as
multiple of 3 the first number that you
could identify the 6 6 is a multiple of
2 and 6 is also a multiple of 3 the next
number is 12 it is a multiple of 3 and
it is also a multiple of 2 18 again a
common multiple 24 is another common
multiple so what are you observing there
are certain multiples which are common
to numbers common to two or more than
two numbers so these num
are said to have common multiple so you
can say that two and three have certain
common multiples so what we can see we
can see that common multiples of two and
three and six 12 18 24 nurses here I
have written only till here if we keep
writing mode we will continue to get
more common multiples so this is the
range of the common multiples of 2 & 3
now what about common factors do you
think that 2 & 3 might have common
factors as well do you think so so for
that let us try to write the factors of
2 what are the factors of T 2 has two
factors 1 & 2 because 2 is a prime
numbers it has two factors one is 1 and
the other one is itself that is 2
similarly factors of 3 would be 1 & 3 so
do you have any common factor yes of
course 1 is a common factors 1 is a
factor of 2 and 1 is also a factor of 3
so therefore we would say that common
factor between 2 & 3 is 1 so they have
just one common factor now anything we
have learned before that the number of
factors for a number is always finite
there a fixed number of factors so it is
quite obvious that the number of common
factors will also be fixed but in case
of multiples there there exists infinite
number of multiples for any number and
therefore the common multiples are also
like many so this is the concept of
common factors and multiples now to have
a better understanding let us try to
find out common factors and multiples of
these 2 numbers 4 & 8 so how will we do
that so again in a similar way first we
will write down multiples of 4 and on
the other side we will write down the
my nipples of eight so it would go
somewhat like this in a similar way we
will like write the multiples of eight
as well so this would be 8 16 24 32 40
48 56 and so on so now can you find out
the common multiples the first common
multiple is 8 next common multiple would
be 16 next one is 24
next is 32 next is 40 and so on
similarly 48 would also come here 4 into
12 would be 48 and so on so therefore we
can say that common multiples between 4
& 8 would be 8 16 24 32 40 and so on so
these are the common multiples now you
might ask what about factors so for that
we will have to determine the factors
first so what are the factors of number
4 it has 1 2 4 because 4 can be written
as 1 into 4 2 into 2 4 ones are 4 so
based on this you can say that 1 2 & 4
are factors of 4 similarly what are the
factors of 8 8 can be written as 1 into
8 2 into 4 4 into 2 8 into 1 so it has 1
2 4 8 so which are the common factors so
basically 1 2 4 these are common factors
so you can say that common factors of 4
& 8 & 1 2 & 4 so in this fashion we can
find out the common factors and
multiples of 2 or more numbers so let us
try with a set of 3 numbers so here you
are asked to find out the common factors
and multiples of 3 numbers 5 15 and 25
so here also we will follow a similar
approach where we will first write down
multiples of each of these numbers so
multiples of 5 then multiples of 15 and
then multiples of 25 similarly when we
write down multiples of 15 it would be
something like this 15 30 45 60 75 90
105 120 135 150 and so on again when you
write down the multiples of 25 it starts
with 25 into 1 which is equal to 25 then
25 to 50 25 3 is 75 25 force 125 into 5
plus 125 25 into 6 is equal to 150 and
so on now looking at these tables can
you identify the common multiples the
first common multiple now a common
multiple would mean that that number
should be a multiple of all the three
numbers for example look at 30 so 30 is
a multiple of 15 30 is also multiple of
5 but that is not a multiple of 25 so 30
will not be considered as a common
multiple of the three numbers so common
means it has to be a multiple of all the
three numbers now let us consider the
number 75 the 75 is a multiple of 25 75
is also a multiple of 15 and 75 is also
a multiple of 5 so the first common
multiple would be 75 the next common
multiple would be 150 because 150 again
is present in all of them Here I am NOT
written till 150 but in this case also
150 is a multiple of 5 5 into 30 is
equal to 150 so therefore in this case
we can write the common multiples
between 5 15 and 25 would go somewhat
like this 75 then 150 and so on
and what about the factors so for
factors again we need to find them first
so 4 5 there are just 2 factors 1 and 5
for 15 we do have more factors like 1 3
5 and 15 these are the factors for 15
because 15 can be written as 1 into 15 3
into 5 5 into 3 and 15 in proven these
are the various ways in which we can
write 15 the third number is 25 so 25
again has various factors like 1 5 and
25 because 25 can be written as 1 into
25 5 into 5 and 25 into 1 so these are
the factors now out of these which are
the common factors 1 is a common factor
and 5 is also a common factor so
therefore common factors between 55 15
and 25 would be 1 and 5 so in this way
we can find out common factors and
multiples between two or more than two
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