Given that HCF (306, 657) = 9, find LCM (306, 657).
Step-by-Step Solution
Key Concept: For any two positive integers a and b, the product of their Highest Common Factor (HCF) and Lowest Common Multiple (LCM) equals the product of the numbers themselves: \(\text{HCF}(a,b) \times \text{LCM}(a,b) = a \times b\).
Given: \(\text{HCF}(306,657) = 9\).
To Find: \(\text{LCM}(306,657)\).
Step 1: Write down the relation between HCF and LCM.
\[\text{HCF}(306,657) \times \text{LCM}(306,657) = 306 \times 657\]
Step 2: Substitute the known HCF value.
\[9 \times \text{LCM}(306,657) = 306 \times 657\]
Step 3: Compute the product of the two numbers.
\[306 \times 657 = 201042\]
Step 4: Solve for LCM.
\[\text{LCM}(306,657) = \frac{201042}{9}\]
Step 5: Perform the division.
\[\frac{201042}{9} = 22338\]
Conclusion: The LCM of 306 and 657 is 22338.
Correct Answer: 22338