English language

How to pronounce 693 in English?

Full Transcript

let's see what question we have over
here
given that the hcf of 12 comma 18 is 6
find the lcm
okay so i'm being given the cf of two
numbers and i have to find the lcm
the first question that strikes me
when i say read this question is why did
you give me the hcf i already know how
to find the lcm if i know both these
numbers
i just have to prime factorize 12 write
it in its prime factorized form write 18
its prime factorized form take each the
highest powers of each of those prime
factors and i'll get my lcm
that's definitely a way you can do this
problem
but because they're giving us the hcf
the question is giving us a clue hey can
you try this other method that you know
of
there is another way to solve this it's
a shorter way are you aware of this
there is a relationship between the hcf
and the lcm
uh
think about that can you recollect it
the relationship is this if you have two
numbers
right this is a headsave of these two
numbers right and you have to find the
lcm of these two numbers the key key
term here is two numbers okay so if you
have the hcf of two numbers let's say
head cf
and then you have the lcm
of two numbers of the same two numbers
of course and then if you have this
other quantity which is just the product
of these two numbers i'm just going to
call it the product
of the two numbers
two numbers
so these three are three quantities
right hcf you know how to find lcm you
know how to find product you've always
known how to find you have to multiply
these two then there is a relationship
between these
and it's like the hcf into the lcm the
product of the hcf and lcm will be equal
to the product of the two numbers
now pause for a moment
that's beautiful if you think about it
why this works if you have a lot of
questions around this we will talk about
that in a later video but just notice
that this is actually going to make our
problem much simpler
right
so if you believe this to be true it's
in the book so let's believe for now
that this is true hit safe into lcm
equals equals product of the two numbers
then how will you solve this question
you don't have to prime factorize all
this now because all you'll say is oh
headsafe is given to me
hetf is six
so that's given
that multiplied by lcm which is what i
need to find
lcm
will be equal to the product of the two
numbers and the two numbers here are 12
and 18. so 12 times 18
and with this i can find my lcm i'm
going to divide both sides by let's
write 6 so that i have lcm
equals i divide this side by 6 and then
i divide this side by 6 i get 12 times
18 divided by 6
and we can find the answer to that 6 and
12 would be
this goes like 2 times 6 is 12. so i'm
dividing by 6 in the numerator and
denominator and you have 18 times 2
which is
36.
so the lcm of
these two numbers 12 and 18 is 36 but
you didn't do it in the usual method
that you're used to you did it this time
using this new property or this new
result so let's say it's like this is
actually the main
point of this video
the main point of this video is to uh
help you uh know this result that here
into lcm equals product of the two
numbers now what i want to do is really
highlight this two over here okay
the key term here is this two
because if this had been three numbers
if you had been given the hcf of 12 18
comma something else
so all three numbers that hit cf is six
find the lcm you cannot do this happen
to lcm will not be the product of those
three numbers so two is really the key
word here so as long as the question has
only two numbers in it here of two
numbers then this result works which
must raise the question right why why is
it that's the result this looks so
beautiful only works for two numbers
think about that i mean it's a great
question to think about uh while you do
that right one of the best ways to get
comfortable thinking about these things
is just solve one or two more problems
do using that so let's do that let's
solve one more question where we use
this property
now in this question i have hcf of two
numbers is 11 and the lcm is 693. so
both the hcf and the lcm are given to me
one of the numbers is 99 find the other
number
now how do you want to think about this
question you just learned the new
property so your mind might be thinking
oh i can definitely use it just before
you conclude that always verify hey
there's two numbers so it'll work if
it's three or four or five it won't work
so it's two numbers so yeah we can use
that property and what is our property
the hcf
multiplied by the lcm
will be equal to the product of the two
numbers maybe for now we can call these
two numbers say
uh n1 and n2 i just see the sounding
names for the just the two numbers that
we're looking for so in this question
what they're doing is that they're
giving us the hits of an lcm and one of
the numbers and asking us for
the other number so you can pause right
now because after this it's about
putting the numbers right in
and finding the answer to the number
that we want
i'm going to do it now so head cf is
what hits af is 11. so hcf is 11.
multiplied by lcm is 693
693 one of the numbers is 99
99
and the other number is what we want so
now i'm just going to call it yeah n2
maybe so how do i do this now i'm going
to divide both sides of the equation by
99 so that will give me
n2
and 2 equals i'm just bringing all this
here okay or actually i can keep this
on this side
itself it doesn't matter right so 11
into 693 11 into 693 divided by 99 693
divided by
the 99 that i divided both sides by so
99 and maybe we can go left side now so
what happens here
so i know that 11 and 99 are nicely
divisible so this is 9 times 11 so i
have this
9 and 6 93 it should probably be
divisible because we're looking for a
natural number so 69 uh 9 goes what
seven nine sevens are 63 so seven times
uh you have what um 69 so we have six
remaining 63 or 77
so there we have it the other number is
77
i can try it on this side also 77
and we have it
so
this new property as you can see is
pretty useful um if not for anything
else in the real life at least to answer
many questions where we know
three of these things and we're asked to
find one of them so all the questions
you will see in fact most of the
questions you will see where will be
where you're given
the hcf lcm and one of the numbers or
lcm and two of the numbers or hcf and
two of the numbers that's pretty much
the types of questions we can be uh
asked over here so you don't have to
really practice hundreds of questions
here right because you know all of the
problems are going to be in this format
you just have to find out which of the
three you have and find the other one
so that's that's pretty much all we have
to cover in this particular property
except one big question which is hey why
is this probably true
why why does this work
um can we have oh no that was a big ink
smudge so why does this property work
and also asking why does it all only
work for two numbers like the same thing
is become n into n one and two into n
three into n four or something this
doesn't work so why is that the case and
i'm going to cover that in a separate
video maybe i'll call that um a head cf
and lcm product or visualize to
something uh the clue for you though
before you watch that video i want you
to think about this and the clue is that
just think about what the hcf really is
so when you prime factorize two numbers
and find the heads here what are you
really doing you're picking the minimum
powers of each of the prime factors and
the lcm you're picking the maximum
powers
right
so think about what you're really doing
when you're doing that and then think
about what the product is in the same
way
like when you prime factorize the two
numbers and think about what the product
is and when you think about it you'll be
able to see oh so that's why it works in
the case of two numbers and why it
doesn't work in the case of higher
numbers

let's see what question we have over

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How to pronounce 693 in English?

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