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Two numbers are in the ratio 6:13. if their LCM is 312, what are the two numbers?

Let the required numbers be 6x and 13x

Then their L.C.M. is 

So,

Thus,

The numbers are  and 

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Let first no.= 6y

Let 2nd no.= 13y

We know that, LCM of two coprime numbers = Product of two coprime numbers

Since 6 and 13 are coprime numbers

6y*13y = 78y = 312

y = 312/78

y= 4

So, first number = 6y = 6*4 = 24

second number = 13y = 13*4 = 52

Hope, this answer help you

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