Question

Three numbers in the ratio 2:3:4 have their sum 270. Then the L.C.M. is

• A. 120
• B. 360
• C. 240
• D. 270

Hint:

When the numbers are given in a ratio, express them in terms of a common variable and solve for the unknown. Then, find the LCM.

Answer 1

The Correct Option is B

Let the three numbers be \( 2x \), \( 3x \), and \( 4x \). The sum of these numbers is given as 270: \[ 2x + 3x + 4x = 270 \quad \Rightarrow \quad 9x = 270 \quad \Rightarrow \quad x = 30. \] So, the numbers are \( 2x = 60 \), \( 3x = 90 \), and \( 4x = 120 \). Now, the L.C.M. of 60, 90, and 120 is: \[ \text{L.C.M.} = 360. \]