The LCM of two numbers is 90 whereas their HCF is 6 If one number is 12 more than the other then the...........

Quantitative Aptitude (MTS) LCM, HCF

The LCM of two numbers is 90, whereas their HCF is 6. If one number is 12 more than the other, then the greater number is:

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SSC MTS 27th October 2021 Shift-1

- Let's call the two numbers \( x \) and \( y \), where \( x < y \) and \( y = x + 12 \).

- The given LCM (Least Common Multiple) of \( x \) and \( y \) is 90.

- Their HCF (Highest Common Factor) is 6.

- There is a relationship: \( \text{LCM} \times \text{HCF} = x \times y \).

- Using the relationship: \( 90 \times 6 = x \times y \).

- So, \( 540 = x \times y \).

- Substitute \( y = x + 12 \) into the equation: \( x \times (x + 12) = 540 \).

- Solving: \( x^2 + 12x - 540 = 0 \).

- Factor the quadratic: \((x - 18)(x + 30) = 0\).

- So, \( x = 18 \) (since \( x > 0 \)), thus \( y = 30 \).

- Correct Answer: 30

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