Question

If the ratio of two numbers is 11 : 12 and their LCM is 528, then their H.C.F is:

• A. 4
• B. 2
• C. 8
• D. 16

Hint:

To find the HCF of two numbers when the ratio and LCM are given, use the relation: \[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b. \]

Answer 1

The Correct Option is A

Let the two numbers be \( 11x \) and \( 12x \), where \( x \) is the common factor.
We know the formula for LCM and HCF of two numbers \( a \) and \( b \): \[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b \] So, for the given numbers \( 11x \) and \( 12x \), we have: \[ \text{LCM}(11x, 12x) \times \text{HCF}(11x, 12x) = (11x) \times (12x) \] \[ \text{LCM}(11x, 12x) = 528, \quad \text{so} \] \[ 528 \times \text{HCF}(11x, 12x) = 11 \times 12 \times x^2 \] \[ 528 \times \text{HCF}(11x, 12x) = 132x^2 \] \[ \text{HCF}(11x, 12x) = \frac{132x^2}{528} = \frac{x^2}{4} \] Since \( x^2 \) must be a perfect square and the HCF must be a common divisor of 11 and 12, \( x = 2 \). Thus, \[ \text{HCF}(11x, 12x) = 4. \]