Question

Given that LCM of \( (132, 288) = 3168 \), then HCF of \( (132, 288) \) will be:

• A. 288
• B. 132
• C. 48
• D. 12

Hint:

The HCF and LCM of two numbers are related by the formula: \[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b. \]

Answer 1

The Correct Option is D

We know the relationship between LCM, HCF, and the product of two numbers: \[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b \]
Step 1: Substitute the known values.
We are given: - \( \text{LCM}(132, 288) = 3168 \) - \( a = 132 \) - \( b = 288 \) Using the formula: \[ 3168 \times \text{HCF}(132, 288) = 132 \times 288 \]
Step 2: Simplify the equation.
First, calculate \( 132 \times 288 \): \[ 132 \times 288 = 37956 \] Now, solve for \( \text{HCF}(132, 288) \): \[ 3168 \times \text{HCF}(132, 288) = 37956 \] \[ \text{HCF}(132, 288) = \frac{37956}{3168} = 12 \]
Step 3: Conclusion.
Therefore, the HCF of \( 132 \) and \( 288 \) is 12.