HCF & LCM Using Prime Factorisation

 

❓ Question

Find the HCF of 96 and 404 by prime factorisation method.
Hence, find their LCM.

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🖼️ Solution Image

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✍️ Short Solution

This is a prime factorisation + HCF–LCM relation question.
Use:

• HCF → smallest power of common factors
• LCM → (a × b) / HCF 💯

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🔹 Step 1 — Prime Factorisation

$$96=2^5\times 3$$
$$404=2^2\times 101$$

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🔹 Step 2 — Find HCF

👉 Common prime factor = 2

$$\text{HCF}=2^{\min (5,2)}=2^2=4$$

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🔹 Step 3 — Use Relation to Find LCM

$$\text{LCM}\times \text{HCF}=𝑎\times 𝑏$$
$$\text{LCM}\times 4=96\times 404$$
$$\text{LCM}=\frac{96\times 404}{4}$$
$$\text{LCM}=96\times 101=9696$$

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🔹 Step 4 — Final Values

$$\text{HCF}=4$$
$$\text{LCM}=9696$$

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✅ Final Answer

$$\boxed{{\displaystyle \text{HCF}=4,\text{ LCM}=9696}}$$

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⭐ Key Insight

• HCF → common lowest power
• LCM → can be found using relation

🧠 Memory Line:

LCM × HCF = Product of numbers