Question

The ratio of two numbers is $3:4$ and their H.C.F. is $4.$ What is their L.C.M.?

• A. $12$
• B. $16$
• C. $24$
• D. $48$

Answer 1

The correct option is D $48$

Let the numbers be $3x$ and $4x$ then their $H.C.F=x$ as $3$ and $4$ are coprime numbers hence $3x$ and $4x$ have $x$ in common therefore $x$ is the HCF of $3x$ and $4x$

$H.C.F=4$ (Given)

$\Rightarrow x=4$

$\Rightarrow 3x=12$ and $4x=16$

$\therefore$ numbers are $12$ and $16$

$\Rightarrow L.C.M=48$