Question

The H.C.F and L.C.M of the numbers, $\frac{1}{2}$, $\frac{2}{3}$, $\frac{3}{5}$ is

• A. H.C.F. $=\frac{2}{30}$ and L.C.M. $=\frac{1}{30}$
• B. H.C.F. $=\frac{1}{60}$ and L.C.M. $=6$
• C. H.C.F. $=\frac{1}{30}$ and L.C.M. $=6$
• D. H.C.F. $=6$ and L.C.M. = $\frac{1}{30}$

Answer 1

Answer: (C)

H.C.F. $=\frac{1}{30}$ and L.C.M. $=6$

$\frac{1}{2}$, $\frac{2}{3}$, $\frac{3}{5}$.
L.C.M. of fractions $=\frac{L.C.M.ofnumerators}{H.C.F.ofdenominators}$
H.C.F. of fractions $=\frac{H.C.F.ofnumerators}{L.C.M.ofdenominators}$
L.C.M. $=\frac{L.C.M.of(1,2,3)}{H.C.F.of(2,3,5)}$
$L.C.M.of(1,2,3)=6$
$H.C.F.of(2,3,5)=1$
So, $L.C.M.offractions=\frac{6}{1}=6$
H.C.F. of fractions $=\frac{H.C.F.ofnumerators}{L.C.M.ofdenominators}$
H.C.F. $=\frac{H.C.F.of(1,2,3)}{L.C.M.of(2,3,5)}$
$H.C.F.of(1,2,3)=1$
$L.C.M.of(2,3,5)=30$
So, $H.C.F.offractions=\frac{1}{30}$