Three numbers are in the ratio 2 : 3 : 4 and their L.C.M. is 180. Find the sum of the squares of numbers.

Let the numbers be 2x, 3x and 4x.

Their LCM = 3 × 4x = 12x

∴ 12x = 180

$\Rightarrow x=\frac{180}{12}=15$

∴ Sum of the squares of numbers

= (2x)² + (3x)² + (4x)² = 4x² + 9x² + 16x²

= 29x² = 29 × 15 × 15 = 6525