Question

If $LCM(35, 63) = 315$, the $HCF(35, 63)$ will be:

• A. 5
• B. 7
• C. 9
• D. 11

Hint:

Always remember the relation: $HCF \times LCM = Product$ of the numbers. This is very useful for solving LCM/HCF problems quickly.

Answer 1

The Correct Option is B

Step 1: Relation between LCM and HCF
For two numbers $a$ and $b$: \[ LCM(a, b) \times HCF(a, b) = a \times b \]

Step 2: Apply the formula
Here $a = 35$, $b = 63$, and $LCM(35, 63) = 315$.
\[ HCF(35, 63) = \dfrac{a \times b}{LCM(a, b)} \] \[ HCF = \dfrac{35 \times 63}{315} \] \[ HCF = \dfrac{2205}{315} = 7 \]

Step 3: Conclusion
Thus, the $HCF(35, 63) = 7$.
The correct answer is option (B).