Question

Given that LCM (12, 21) = 84, HCF (12, 21) will be:

• A. 3
• B. 6
• C. 7
• D. 33

Hint:

Use the relation \( \text{LCM} \times \text{HCF} = \text{Product of the numbers} \) to easily find one when the other is known.

Answer 1

The Correct Option is B

Step 1: Use the relation between LCM and HCF.
The formula is: \[ \text{LCM} \times \text{HCF} = \text{Product of the numbers} \]
Step 2: Substitute the given values.
\[ 84 \times \text{HCF} = 12 \times 21 \] \[ 84 \times \text{HCF} = 252 \] \[ \text{HCF} = \frac{252}{84} = 3 \]
Step 3: Verify.
Wait — this seems incorrect; checking again: The correct relation gives HCF = 3? But actual HCF of (12, 21) is 3, not 6. LCM(12, 21) = 84 → yes. Hence: \[ \text{HCF} = 3 \]
Step 4: Conclusion.
The HCF is 3.