Mathematics-HCF and LCM

H.C.F (Highest Common Factor)  :: -  The H.C.F of two or more than two number is the greatest number that divides each of them exactly. 

There are two methods to finding the H.C.F of numbers.
1) Factorization method. :: - Each one of the given numbers is expressed as product of prime factors.  The product of least powers of common prime factors gives H.C.F .

2) Division method. ::- Divide the large number by smaller one. Then divide the divisor by remainder. Repeat the process untill we get 0 as remainder. Then last divisor is H.C.F

If we want to find the H.C.F of more than 2 numbers, then first find the H.C.F of last two numbers, and its result and first number is used for calculating the whole H.C.F .

L.C.M (Least Common Factor) ::- The least number which is exactly divisible by each one of the given number is called L.C.M.

1) Factorization method. :: - Product of highest powers of all the factors gives L.C.M

Product of two numbers :: - Product of their H.C.F and L.C.M

H.C.F and L.C.M of fractions

H.C.F = H.C.F of Numerators / L.C.M of Denominators

L.C.M = L.C.M of Numerators / H.C.F of Denominators