Question

Find the L.C.M of $\frac{2}{3},\frac{8}{9},\frac{32}{81},\frac{10}{27}$

Answer 1

L.C.M of fractions$=\frac{L.C.Mofnumerators}{H.C.Fofdenominators}$

L.C.M of $(\frac{2}{3},\frac{8}{9},\frac{32}{81},\frac{10}{27})=\frac{L.C.Mof(2,8,32,10)}{H.C.Fof(3,9,81,27)}$

L.C.M of $2,8,32,10$

Factors of $2=2\times 1$

Factors of $8=2\times 2\times 2$

Factors of $32=2\times 2\times 2\times 2\times 2$

Factors of $10=2\times 5$

L.C.M$=2\times 2\times 2\times 2\times 2\times 5=160$

H.C.F of $3,9,81,27$

Factors of $3=3\times 1$

Factors of $9=3\times 3$

Factors of $81=3\times 3\times 3\times 3$

Factors of $27=3\times 3\times 3$

H.C.F$=3$

$\therefore$ L.C.M of $(\frac{2}{3},\frac{8}{9},\frac{32}{81},\frac{10}{27})=\frac{L.C.Mof(2,8,32,10)}{H.C.Fof(3,9,81,27)}$

$=\frac{160}{3}$