Highest Common Factor And Lowest Common Multiple

How to find out H.C.F & L.C.M?

Factors and Multiples: If 'x' divides 'y' exactly we say that 'x' is a factor of 'y'and also we say that 'y' is multiple of 'x'.
factor of 30=1x30,2x15,10x3,5x6.
H.C.F(highest common factor):
The H.C.F of two or more than two numbers is the greatest number that divides each of them exactly.
eg-18,24,42
18=2x3x3
24=2x2x2x3
42=2x3x7 H.C.F the common factor of the number is 2x3=6 so H.C.F is 6.

L.C.M(Lowest Common Multiple):
The least number which is exactly divisible by each one of the given numbers is called L.C.M.

Formula:
 If 1 number is given and H.C.F and L.C.M is given or any three data is given out of four
Number1 x Number2 =H.C.F x L.C.M
Ex.The H.C.F of two number is 96 and their L.C.M is 1296.if one number is 864,find the other
Sol:Number1 x Number2 =H.C.F x L.C.M
          864 x number2 = 96x1296
       number2=144.

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

* L.C.M=L.C.M of numerators / H.C.F of denominators

Ex.2/3,4/9,5/6 find L.C.M?
Sol: L.C.M=L.C.M(2,4,5)/H.C.F(3,9,6)=20/3

* H.C.F=H.C.F of numerators/L.C.M of denominators

Ex.3/4,6/25,12/35,3/5 find the H.C.F?
Sol: H.C.F=H.C.F(3,6,12,3)/L.C.M(4,25,35,5)=3/700