# Q.11. Three numbers are such that the first is $\frac{1}{3}$ of the second and the third is $\frac{2}{5}$ of the sum of the first and second. If their LCM is 120, then find the third number.

Please find below the solution to the asked query:

Let , first number =

*x*, So from given condition we get :

Second number = $\frac{x}{3}$

And from second condition we get :

Third number = $\frac{2}{5}\left(x+\frac{x}{3}\right)=\frac{2}{5}\left(\frac{3x+x}{3}\right)=\frac{2}{5}\left(\frac{4x}{3}\right)=\frac{\mathbf{8}\mathbf{}\mathbf{x}}{\mathbf{15}}$

Also given : L.C.M. of these three numbers = 120

And we know L.C.M. of fractions = $\frac{\mathrm{L}.\mathrm{C}.\mathrm{M}.\mathrm{of}\mathrm{Numerator}}{\mathrm{H}.\mathrm{C}.\mathrm{F}.\mathrm{of}\mathrm{Denominator}}$

So,

L.C.M. (

*x*,

*x*and 8

*x*) = 8

*x*

And

H.C.F ( 1 , 3 and 15 ) = 1

So,

8

*x*= 120 ,

*x*= 15

Then,

First number = 15 , Second number = $\frac{15}{3}$ = 5 and

**Third number = $\frac{8\times 15}{15}$ = 8 ( Ans )**

Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards

**
**