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Given:

Ratio of the numbers = 2/3 LCM of numbers = 180 Formula used: Product of LCM and HCF of two numbers is equal to the product of the numbers

HCF = ?

LCM × HCF = a × b (a, b are the two numbers)

Let, numbers = 2x and 3x

LCM = 2 x 3 x x = 6x

.. 6x = 180

x = 180/6 = 30

Numbers are 30 * 2 = 60 and 30 * 3 = 90

Now, LCM × HCF = ab (a, b are the numbers)

.. 180X = 60 * 90

.. X = 5400/180 = 30

Therefore, HCF = 30

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