Question

Calculate LCM of $\frac{2}{3},\frac{5}{12},\frac{10}{27}$ and $\frac{4}{21}$ using long division method.

• A. $\frac{5}{3}$
• B. $\frac{10}{3}$
• C. $\frac{20}{3}$
• D. $\frac{40}{3}$

Answer 1

The correct option is C $\frac{20}{3}$

We have to find the LCM of $\frac{2}{3},\frac{5}{12},\frac{10}{27},\frac{4}{21}$ by long division method.

We know that LCM of fractions$=\frac{\text{LCM of numerator}}{\text{HCF of denominator}}$

Now let us find the LCM of numerator: $2,5,10,4$

Thus the LCM of numerator is $2\times 2\times 5=20$

Now let us find the HCF of denominator: $3,12,27,21$

Thus the HCF of denominator is $3$.

Hence, LCM of fractions$=\frac{\text{LCM of numerator}}{\text{HCF of denominator}}=\frac{20}{3}$