Abstract: In the basic mathematics H.C.F and L.C.M
are an important concept related to factors or multiples
of numbers . The calculation of H.C.F or L.C.M mainly
follows the factorization of given numbers into prime
numbers. The largest common factor of two or more
numbers is called the highest common factor (HCF).
Lowest Common Multiple is the smallest positive
number that is a multiple of two or more numbers. In the
present paper it is tried to show that the whole theory
follows the completeness property of real numbers.