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Two numbers are in the ratio of $3 : 4$ . If their LCM is $180$ , then the numbers are and .

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Detailed Solution

Two numbers are in the ratio of 3:4. If their LCM is 180, then the numbers are 45 and 60.
It is given that, two numbers is in the ratio

3 : 4

180

is their LCM.
Let

3 x

and

4 x

be the required numbers.
Therefore, LCM of

3 x, 4 x

12 x

.
It is also given that the LCM is

180

12 x = 180

x = 15

Therefore, the numbers are,

3 x = 3 × 15 = 45

And

4 x = 4 × 15 = 60

The numbers are

45, 60

.
Hence, the required answer is 45 and 60.

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