Two numbers are in the ratio 2 : 3. If their L.C.M. is 48. what is sum of the numbers?

Two numbers are in the ratio 2 : 3. If their L.C.M. is 48. what is sum of the numbers?
A. 28 B. 40
C. 64 D. 42

Answer: Option B

Explanation:

Let the numbers be $2x$ and $3x$

LCM of $2x$ and $3x$ $=6x$ (∵ LCM of 2 and 3 is 6. Hence LCM of $2x$ and $3x$ is $6x$)

Given that LCM of $2x$ and $3x$ is 48

=> $6x=48$
=> $x=\frac{48}{6}=8$

Sum of the numbers
$=2x+3x=5x$
= 5 × 8 = 40