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