Question

If two numbers are in the ratio $6:13$ and their least common multiple is $312$, then find the sum of those numbers.

Answer 1

Given ratio of the numbers = $6:13$

Let the numbers be 6x and 13x

LCM of these two numbers is given as 312

And 6x and 13x are co-prime nos.

$\therefore L.C.M.(6x,13x)=(6\times 13)\times x=78x$

L.C.M of the numbers $=312$

$78x=312$

$X=4$

The numbers are $6x=6\left(4\right)=24$

And $13x=13\left(4\right)=52$

therefore sum of numbers is $52+24=76$