Question

Find the LCM of $2\frac{1}{2}$, $3\frac{1}{3}$ and $1\frac{1}{4}$.

• A. $10$
• B. $15$
• C. $\frac{5}{2}$
• D. $\frac{1}{10}$

Answer 1

The correct option is A

$10$

The Least Common Multiple (LCM) of a group of numbers is the smallest number that is a multiple of all the numbers.
Given mixed fractions can be converted to improper fractions as shown below.
$2\frac{1}{2}=\frac{5}{2}$
$3\frac{1}{3}=\frac{10}{3}$
$1\frac{1}{4}=\frac{5}{4}$
LCM of fractions $=\frac{\text{LCM of numerators}}{\text{HCF of denominators}}$
LCM of numerators 5, 10, and 5 = 10
HCF of denominators 2, 3, and 4 = 1
$\therefore$ LCM of the given numbers =$\frac{10}{1}$ = 10