One fourth of a number added to one-sixth of it is 15. Find the number

The correct answer is 36

Let the number be x
∴ One fourth of the number = $\frac{x}{4}$ and one-sixth of the number = $\frac{x}{6}$
∴ $\frac{x}{4}$ + $\frac{x}{6}$ = 15
Taking L.C.M. of the denominators
$\frac{x*6}{4*6}$ + $\frac{x*4}{6*4}$ = 15
$\frac{6x}{24}$ + $\frac{4x}{24}$ = 15
$\frac{6x + 4x}{24}$ = 15
Multiplying by 24 on both sides
10x = 15 * 24
10x = 360
∴ x = 36