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Highest Common Factor (H.C.F) : It is also called

Greatest common Diviser (G.C.D). When a greatest number

divides perfectly the two or more given numbers then that

number is called the H.C.F. of two or more given numbers.

e.g.

The H.C.F of 10, 20, 30 is 10 as they are perfectly

divided by 10,5 and 2 and 10 is highest or greatest of

them.

Least common Multiple (L.C.M.) : The least number

which is divisible by two or more given numbers, that least

number is called L.C.M. of the numbers.

L.C.M. of 3,5,6 is 30, because all 3 numbers divide

30, 60, 90, …… and so on perfectly and 30 is minimum of

them.

Factor and Multiple : If a number m, divides perfectly

second number n, then m is called the factor of n and n is

called the multiple of m.

Rule 1 : 1st number × 2nd number = L.C. M. × H.C.F.

l There are two methods for calculating the H.C.F

and L.C.M.

(i) Factor Method

(ii) Division Method

l If the ratio of two numbers is a:b, (lowest form i.e.

indivisible to each other) then

Numbers are ak and bk, where k is a constant and

hence,

H.C.F. is K and L.C.M. is abk

Rule 2 :

L.C.M of fractions=L.C.M.of numerators/

H.C.F.of denominators

Rule 3 :

H.C.F. of fractions=H.C.F of numerators/

L.C.M.of denominators

l If there is no common factor between two numbers,

then L.C.M. will be the product of both numbers.

l If there are ‘n’ numbers in a set and H.C.F. of any two

numbers is H and L.C.M. of all ‘n’ numbers is L, then

product of all ‘n’ numbers is [(H)^n-1×L].