Question

The LCM of $\frac{8}{9},\frac{20}{27}$ and $\frac{25}{54}$ is ?

• A. $7\frac{5}{27}$
• B. $22\frac{2}{9}$
• C. $5\frac{3}{27}$
• D. $8\frac{11}{9}$

Answer 1

The correct option is B $22\frac{2}{9}$

L.C.M of $9,27$ and $54$ is $54$
Multiply Numerator and Denominator of first fraction by $\frac{54}{9}=6$

First fraction $\frac{8}{9}\times \frac{6}{6}=\frac{48}{54}$

Multiply Numerator and Denominator ofsecond fraction by $\frac{54}{27}=2$

Second fraction $\frac{20}{27}\times \frac{2}{2}=\frac{40}{54}$

Multiply Numerator and Denominator ofthird fraction by $\frac{54}{54}=1$

Third fraction $\frac{25}{54}\times \frac{1}{1}=\frac{25}{54}$

Now, since all denominators are same, LCM of numerators $48,40,25$ is $1200$
Hence, L.C.M of $\frac{48}{54},\frac{40}{54}$ and $\frac{25}{54}$ is $\frac{1200}{54}=\frac{200}{9}=22\frac{2}{9}$

Hence, option B.