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The LCM of two numbers is 70 times their HCF. The sum of LCM and HCF is 1917. If one of the numbers is 210, then what is the sum of two numbers?

The LCM of two numbers is 70 times their HCF. The sum of LCM and HCF is 1917. If one of the numbers is 210, then what is the sum of two numbers? Correct Answer 453

Given:

LCM of two numbers = 70 × HCF of two numbers

Sum of LCM and HCF = 1917

One of the two numbers = 210

Concept used:

Product of two numbers = LCM × HCF

Calculation:

Let the HCF of two numbers be x.

LCM of two numbers = 70x

According to the question

LCM + HCF = 1917

⇒ (x + 70x) = 1917

⇒ 71x = 1917

⇒ x = 27

HCF of two numbers = 27

LCM of two numbers = 70 × 27

⇒ 1890

Now, we know that

Product of two numbers = LCM × HCF

⇒ (210) × (Second Number) = 1890 × 27

⇒ Second Number = (51030/210)

⇒ Second Number = 243

Sum of two numbers = (210 + 243)

⇒ 453

∴ The Sum of two numbers is 453.

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