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There are two numbers A and B (A > B) of two-digits each and their HCF is 18. If LCM and HCF of B and 45 are 270 and 9 respectively and the difference between digits of A is 5, then what is the LCM of A and B?

There are two numbers A and B (A > B) of two-digits each and their HCF is 18. If LCM and HCF of B and 45 are 270 and 9 respectively and the difference between digits of A is 5, then what is the LCM of A and B? Correct Answer 216

Given:

LCM and HCF of B and 45 are 270 and 9 respectively.

Formula Used:

First number × Second number = HCF × LCM

Calculation:

B × 45 = 9 × 270

⇒ B = 54

∵ HCF of A and B is 18 and A is greater B.

⇒ Possible values of A = 72 and 90

∵ The difference between the digits of A is 5. So, the value of A must be 72.

∴ LCM of A and B = LCM of 72 and 54

= 216

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