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The Ratio of the value of two numbers P to Q is 5 : 7 and the difference between HCF and LCM of P and Q is 578. If LCM of P and Q is ‘a’, then what is the HCF of ‘a’ and 357?

The Ratio of the value of two numbers P to Q is 5 : 7 and the difference between HCF and LCM of P and Q is 578. If LCM of P and Q is ‘a’, then what is the HCF of ‘a’ and 357? Correct Answer 119

Given:

LCM – HCF = 578

Calculation:

Let the value of P and Q be ‘5x’ and ‘7x’ respectively.

⇒ HCF of P and Q = HCF of ‘5x’ and ‘7x’ = x

⇒ LCM of P and Q = LCM of ‘5x’ and ‘7x’ = 35x

According to the question:

35x – x = 578

⇒ 34x = 578

⇒ x = 17

LCM of P and Q = a = 35x

⇒ a = 595

∴ HCF of ‘a’ and 357 = HCF of 595 and 357

= 119

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