Just now, an expert has given comprehensive answer about the usage of LCM and HCF.  In fact, my question was whether 'Least Common Factor' [LCF] and 'Highest Common Multiple'{HCM} exist in Maths? If so, what are their usage?

Dear Student,

Firstly talking about highest common multiple HCM, consider two numbers 3 and 4.
Their common multiples are 12, 24, 36, 48, and so on.
Is it possible to define the greatest number in this pattern?
The answer is No!. We can't terminate this sequence at any point and hence no greatest such number.
Thus there does not exist any HCM.

Now, least common factor LCF. 
It is possible to define LCF for any two numbers.
In case the numbers are co-prime, the LCF=1 and if they are not co-prime we will get some prime number as the answer which is smallest of all primes which divide both the numbers. So it does not have any significance on whole, but may be used in some extreme cases.

Hope this information will clear your doubts about topic.

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