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Two numbers are in the ratio 3 ∶ 5. If their LCM is 105, what is the HCF?
1. 14
2. 20
3. 7
4. 21

1 Answer

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Correct Answer - Option 3 : 7

Given:

Ratio of two numbers = 3 ∶ 5

LCM = 105

Calculation:

Let, the numbers = 3x and 5x

According to the question,

⇒ 3x = 3 × x

⇒ 5x = 5 × x

∴ LCM of 3x and 5x = (3 × 5 × x) = 15x

∴ HCF of 3x and 5x = x

According to the question,

⇒ 15x = 105

⇒ x = 7

∴ HCF = 7

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