Question

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

Answer 1

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★ Let the required number be 6x and 13x.

So, their LCM is 78x.

So,
⇒ 78x = 312
⇒ x = 312/78
⇒ x = 4

The required numbers are

⇒ 6x
⇒ 6 × 4
⇒ 24

and

⇒ 13x
⇒ 13 × 4
⇒ 52

★ The two numbers are 24 and 52.

Answer 2

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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


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