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Three number are in the ratio of 3 ∶ 5 ∶ 7 and their LCM is 420. Find their HCF.
1. 4
2. 3
3. 7
4. 5

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Correct Answer - Option 1 : 4

Given:

The ratio of three numbers =  3 ∶ 5 ∶ 7

LCM = 420

Calculation:

Let the number be 3x, 5x and 7x.

LCM of (3x, 5x and 7x) = 3 × 5 × 7 × (x)

LCM of (3x, 5x and 7x) = 105x

According to the question,

105x = 420

⇒  x = 4

HCF of (3x, 5x, and 7x) = x = 4

Here, x is the common factor of three numbers.

∴ The HCF of the three numbers is 4.

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