LCM × HCF = Product of Numbers Explained

 

❓ Question

Given that:

$$\text{HCF}(306,657)=9$$

Find:

$$\text{LCM}(306,657)$$

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🖼️ Solution Image

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✍️ Short Solution

This is a direct HCF–LCM relation question.

Use the formula:

$$\text{LCM} \times \text{HCF} = a \times b$$

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🔹 Step 1 — Write the Formula

For any two integers $a$ and $b$:

$$\text{LCM} \times \text{HCF} = a \times b$$

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🔹 Step 2 — Substitute Values

Given:

$$\text{HCF} = 9$$
$$a = 306,\quad b = 657$$

So,

$$\text{LCM} \times 9 = 306 \times 657$$

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🔹 Step 3 — Find LCM

$$\text{LCM} = \frac{306 \times 657}{9}$$
$$\text{LCM} = \frac{201042}{9}$$
$$\text{LCM} = 22338$$

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✅ Final Answer

$$\boxed{\text{LCM}(306,657)=22338}$$

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⭐ Key Insight

For any two numbers:

$$\boxed{\text{LCM} \times \text{HCF} = \text{Product of the numbers}}$$

🧠 Memory Line:

LCM nikaalne ke liye product ko HCF se divide karo