If two numbers are in the ratio 6 : 13 and their L.C.M. is 312, find the numbers.

Given:

Two numbers are in the ratio 6 : 13 and their L.C.M. is 312.

To do:

We have to find the numbers.

Solution:

Let the numbers be $6x$ and $13x$.

This implies,

LCM of the numbers $6x$ and $13x=6\times13\times x$

$=78x$

Therefore,

$78x=312$

$x=\frac{312}{78}$

$x=4$

$\Rightarrow 6x=6(4)=24$

$\Rightarrow 13x=13(4)=52$

The numbers are $24$ and $52$.

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Updated on: 10-Oct-2022

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