Given that HCF (306, 657) = 9 , find LCM (306, 657)

Answer

To find the LCM (Least Common Multiple) of the numbers 306 and 657 given that their HCF (Highest Common Factor) is 9, we can use the relationship between LCM and HCF:

**Step 1: Use the relationship between LCM, HCF, and the two numbers.**
The formula relating LCM and HCF is:
\[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b \]
where \( a = 306 \) and \( b = 657 \).

**Step 2: Substitute the known values into the formula.**
We know that:
\[ \text{HCF}(306, 657) = 9 \]
So we can substitute this into the formula:
\[ \text{LCM}(306, 657) \times 9 = 306 \times 657 \]

**Step 3: Calculate the product of the two numbers.**
Now, we need to calculate \( 306 \times 657 \):
\[ 306 \times 657 = 201342 \]

**Step 4: Solve for LCM.**
Now we can solve for LCM:
\[ \text{LCM}(306, 657) = \frac{306 \times 657}{9} \]
Substituting the product we calculated:
\[ \text{LCM}(306, 657) = \frac{201342}{9} \]

**Step 5: Perform the division.**
Now, we divide \( 201342 \) by \( 9 \):
\[ 201342 \div 9 = 22318 \]

Thus, the LCM of 306 and 657 is:
\[ \text{LCM}(306, 657) = 22318 \]

### Final Answer:
\[ \text{LCM}(306, 657) = 22318 \]

---