HCF And LCM

H.C.F of factor=       H.C.F of numerators

                                  L.C.M of denominators

L.C.M of factor=       L.C.M of numerators

                                  H.C.F of denominators

Note:-Multiplication  of any two number is always equal two the multiplication of its HCF and LCM.\

  **          first number*second number=HCF*LCM                        eq-1

we know HCF convert numbers in ratio with divide.

for Example we have two number "15 and 28" and the HCF of these numbers is 3.

if we divide numbers with HCF then we find ratio 5:7

Now

if the given number is in ratio of a:b then we can say-

first number=a*HCF

second number=b*HCF

               a*HCF*b*HCF=HCF*LCM                                    from eq-1

**          a*b=LCM/HCF                                                           eq-2

example:- if the HCF of 4 no's is 3 and LCM is 114 then find the multiplication of these numbers.

      

                Assume the ratio of these four no is a:b:c:d then the numbers will be

                3a,3b,3c and 3d.                                                 (number =ratio*HCF)

                

                then the LCM oh these numbers will be 3abc which is given 114

                3abc=114

                then 3a*3b*3c*3d=27*3abc

                                              =  27*114

                                              =  3078

eq-2 is used to find the co-prime pair

co-prime pair:-the pair which HCF is 1 (means there is no common divisor) is called Co-prime pair.

    for example (4,9) is co prime pair.