Question

LCM of several fractions $\frac{LCMoftheirnumerators}{HCFoftheirdenominators}$
HCF of several fractions $\frac{HCFoftheirnumerators}{LCMoftheirdenominators}$

The H.C.F. of $\frac{2}{5}$, $\frac{6}{25}$ and $\frac{8}{35}$

• A. $\frac{2}{5}$
• B. $\frac{24}{5}$
• C. $\frac{2}{175}$
• D. $\frac{24}{175}$

Answer 1

Answer: (C)

$\frac{2}{175}$

Factors of $6=2\times 3$
$8=2\times 2\times 2$
Therefore, H.C.F. of $2,6,8$ is $2$
Now,
Factors of $25=5\times 5$
$35=5\times 7$
Therefore, L.C.M. of $5,25,35$ is $5\times 5\times 7$
$=175$
Therefore, H.C.F. of $\frac{2}{5},\frac{6}{25},\frac{8}{35}$
$=\frac{H.C.F.of2,6,8}{L.C.M.of5,25,35}$
$=\frac{2}{175}$