Question

What is the smallest multiple common for $\frac{2}{5}$, $\frac{8}{15}$ and $\frac{6}{35}$ ?

• A. $\frac{24}{5}$
• B. $\frac{5}{24}$
• C. $\frac{6}{35}$
• D. $\frac{24}{35}$

Answer 1

The correct option is A

$\frac{24}{5}$

The smallest common multiple is LCM of the given numbers. The Least Common Multiple (LCM) of a group of numbers is the smallest number that is a multiple of all the numbers.
LCM of fractions $=\frac{\text{LCM of numerators}}{\text{HCF of denominators}}$
LCM of numerators 2, 8, and 6 is 24.
HCF of denominators 5, 15, and 35 is 5.
$\therefore$ LCM of the given numbers = $\frac{24}{5}$