1.

Two numbers are in the ratio 2 ∶ 3. If their LCM is 180, the HCF of the numbers is:1. 152. 203. 304. 60

Answer» Correct Answer - Option 3 : 30

Given:

Ratio of the numbers = 2 ∶ 3

LCM of numbers = 180

HCF = ?

Formula used:

Product of LCM and HCF of two numbers is equal to the product of the numbers

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

Let, numbers = 2x and 3x

∴ LCM = 2 × 3 × 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)

∴ 180 × X = 60 × 90

∴ X = 5400 / 180 = 30

Therefore, HCF = 30



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