How to find HCF LCM ? - Math, Class 7 Video Lecture

[Music]
hello everyone today we discussed a
brand new chapter of the TF & LCL
at EF the full form of HC f is highest
common factor also known as GCD of
greatest common divisor now there are
various ways to calculate HCl first of
all it is prime factorization and the
other one is division algorithm by prime
factorization now what is the basic
method we make prime factors of the
numbers we take out common factors of
these numbers and multiply them then we
get a HCF for example take numbers 12
and 14 what are the prime factors of 12
prime factors of 12 are 2 2 & 3 prime
factors of 14 are 2 & 7 now if you see
prime factors of 12 and 14 have only 2
as their common center that's why X here
is only 2 as they have only 2 as their
common factor now let's take another
example numbers we take now are 24 and
28 let's look at prime factors of 24
prime factors are 2 2 2 and 3 prime
factors of 28 are 2 2 & 7 now if we look
here we have two pairs of number 2 as
common factors
therefore at three F is 2 into 2 is
equal to 4
next we move forward to division method
let's take numbers 27 and 36 now we
divide 36 by 27 here we get remainder
night but we didn't get a remainder to
be 0 so now 27 which was the divisor
earlier becomes dividend now we divide
it with remainder 9 and we get a
remainder to be 0 now here what we have
to remember is divide continuously until
the time remainder is not equal to 0
second thing divisor becomes the
dividend and remainder becomes divisor
when we are dividing the same way 27th
becomes dividend while remainder 9
became divisor the last remaining
divisor is our ezio here hence 9 is the
last divisor therefore at CF is equal to
9 and let's move forward to LCM healthy
also known as least common multiple how
do we calculate LCA first by prime
factorization second by common division
method prime factorization method now
let's look at prime factorization method
we take numbers 12 and 18 prime factors
of 12 to 2 and 3 prime factors of 18 2 3
& 3
now here what we are looking forward to
is how many times of fractal occurs
maximum times look at prime factor - it
occurs maximum number of times to three
it also occurs maximum number of times -
therefore our LCM is 2 into 2 into 3
into 3 comes out to be 36 next we look
at another example take numbers 30 and
24 prime factors of 32 3 5 prime factors
of 24 - 2 2 & 3 now if we look here 2
occurs maximum 3 times 3 occurs maximum
one time and 5 also occurs maximum fun
time therefore our LZ n becomes 2 cross
2 cross 2 cross 3 cross 5 is equal to
hundred and twenty next we move to
continued division method take numbers
30 and 45 now let's divide them by our
common factor we divide by 2 then by 3
and so on till we get one as quotient
now here the important points are even
if the number is not divisible right in
as it is
no there was number 45 45 was not
divisible by 2
but still we wrote it as it is continue
dividing by prime factors till we get to
1 as quotient now LCM comes out to be 2
into 3 into 3 into 5 which is equal to
19
here are very important points to
remember first at CF into LCM is always
going to be equal to product of two
numbers second a safe is always smaller
than LCM regardless of the thing HCF has
full form as highest common factor and
LCM is least common multiple this is a
very common mistake students commit
please remember HCF is always smaller
than you'll see any third attempt of
given numbers is not greater than any of
the number fourth LCM of the given
numbers is never smaller than any of the
numbers I hope you understood the basics
of HCF at LCL we'll see you soon with
the next lesson on experts thank you