Question

Find the L.C.M. of fractions $\dfrac{5}{{16}},\dfrac{{15}}{{24}},\dfrac{{25}}{8}$
$
  {\text{A}}{\text{. }}\dfrac{5}{{48}} \\
  {\text{B}}{\text{. }}\dfrac{5}{8} \\
  {\text{C}}{\text{. }}\dfrac{{75}}{{48}} \\
  {\text{D}}{\text{. }}\dfrac{{75}}{8} \\
$

Answer 1

Hint- The LCM of numbers is the smallest number which can divide all those numbers. Finding LCM of fraction Is different from integers. In fractions, the LCM is given by LCM of numerators divided by the HCF of the denominators of the fractions.

Complete step by step answer:
We have been given the fraction, $\dfrac{5}{{16}},\dfrac{{15}}{{24}},\dfrac{{25}}{8}$

As we know that, in fractions, the LCM is given by LCM of numerators divided by the HCF of the denominators of the fractions.

So, the LCM of numerators 5, 15, 25 is ${5^2} \times 3 = 75$

And the HCF of the denominators 16, 24, 8 is 8

So, the LCM of given fractions is $\dfrac{{75}}{8}$.

Hence option D is correct.

Note- Whenever we face such types of problems the key point to remember is that we need to have a good grasp over number theory and fractions. In this particular question, the numbers given are fraction and the way to solve them is different as discussed above.