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

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

a) H.C.F = H.C.F  of Numerator

                  L.C.M of Denominator

H.C.F ( x/a,  y/b,  z/c ) =  H.C.F(x, y, z) / L.C.M( a,b,c) .

 

L.C.M ( x/a,  y/b,  z/c) =  L.C.M (x,y,z) / H.C.F(a,b,c).    

 

Find the H.C.F and L.C.M of Fractions:

1) 2/4,  5/6,  10/8.

Answer:

a) H.C.F( 2/4, 5/6, 10/8) = H.C.F( 2, 5, 10)

                                        L.C.M( 4, 6, 8)

 

We need to find H.C.F and L.C.M of numbers.

 

H.C.F: Listing out Factors Method	L.C.M: Listing out Multiples      Method
Factors of 2 = 1, 2. Factors of 5 = 1, 5. Factors of 10 = 1, 2, 5, 10. Common Factors( 2, 5, 10) = 1.         Therefore, H.C.F( 2, 5, 10) = 1.	Multiples of 4 = 4,8,16,20,24,28,32,36,40. Multiples of 6 = 6,12,18,24,30,36,42,48,54,60. Multiples of 8 = 8,16,24,32,40,48,56,64,72,80. L.C.M(4, 6, 8) = 24.

 

H.C.F( 2/4, 5/6, 10/8) = H.C.F( 2, 5, 10)

                                        L.C.M( 4, 6, 8)

 

                                    =   1  .

                                        24 

 

b) L.C.M ( 2/4, 5/6, 10/8) =     L.C.M( 2, 5, 10)

                                                   H.C.F( 4, 6, 8)

 

H.C.F: Listing out Factors Method	L.C.M: Listing out Multiples      Method
Factors of 4 = 1, 2, 4. Factors of 6 = 1, 2, 3, 6. Factors of 8 = 1, 2, 4, 8. Common Factors( 4, 6, 8) = 1,2.          Therefore, H.C.F( 4, 6, 8) = 2.	Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. L.C.M(2, 5, 10) = 10.

 

L.C.M ( 2/4, 5/6, 10/8) =     L.C.M( 2, 5, 10)

                                               H.C.F( 4, 6, 8)

 

                                       =  10  =  5.

                                            2