Hcf(Highest common factor) is very similar to GCD(greatest common divisor) helps us to find highest factors of numbers which should be common or else it would be 1.
On the other hand LCM(lowest common multiple) is taking multiples(for 4 it is 4,8,12)
of all numbers and then select common of between all of then but is should be lowest.
You can see explanation of both of them with some examples in below.
Let us suppose we have 3 numbers 3,6,30
First,we are going to find numbers(factor) which are divisible with give number(of which we intend to find hcf) and then take highest common among them,
for 3 - 3
for 6 - 2,3,6
for 30 - 2,3,5,10,15,30
So,in above the common numbers are 2,3 but in that highes is 3 so HCF will be 3.
Considering same example as above,
We are going to find multiples of all numbers and will check lowest common value among them
for 3 - 3,6,9,12,15...30,33
for 6 - 6,12,18,24,30,36
for 30 - 30,60
So,in above common numbers between 3,6 are 6,12,18,24 ... but here lowest one is 6 and if we consider 30 at the same time 30 will be the answer.
Help us to common or similarity between numbers.And GCD helps us to solve various mathematical problem very quickly.Variety of questions based on hcf & lcm are asked in many competetive exams. You can just verify your manual anwers with this or you can calculate directly from this which can reduce your time. .