Find the LCM (306,1314), if HCF(306,1314)=18

To find the Least Common Multiple (LCM) of two numbers when the Highest Common Factor (HCF) is known, you can use the following formula:

\[
\text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)}
\]

Given:  
\( a = 306 \),  
\( b = 1314 \),  
\( \text{HCF}(306, 1314) = 18 \).

Now, apply the formula:

\[
\text{LCM}(306, 1314) = \frac{306 \times 1314}{18}
\]

Let's calculate that.

\[
306 \times 1314 = 402684
\]

Now divide by 18:

\[
\text{LCM}(306, 1314) = \frac{402684}{18} = 22371.33
\]

Since the LCM must be an integer, let's correct this. There must have been a rounding or exact calculation issue. We'll try again carefully.The Least Common Multiple (LCM) of 306 and 1314, given that their Highest Common Factor (HCF) is 18, is **22,338**.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How do you find the HCF of two numbers?
2. What is the relationship between LCM and HCF?
3. How would you find the LCM if the HCF is not known?
4. Can the LCM ever be smaller than both numbers?
5. What are some real-life applications of finding the LCM?

**Tip:** When two numbers are relatively prime (HCF = 1), the LCM is simply their product!

Learn how to find the Least Common Multiple (LCM) of 306 and 1314 when the Highest Common Factor (HCF) is 18. This step-by-step solution uses the relationship between LCM and HCF, suitable for students in Grades 6-8.

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