Given HCF and Product of Two Numbers, Find Their LCM

Video Explanation

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Solution

Question: The HCF of two numbers is 16, and their product is 3072. Find their LCM.

Step 1: Use the Relation Between HCF, LCM and Product

For any two positive integers a and b,

a × b = HCF (a, b) × LCM (a, b)

Step 2: Substitute the Given Values

3072 = 16 × LCM

Step 3: Calculate the LCM

LCM = 3072 ÷ 16

LCM = 192

Final Answer

∴ The LCM of the two numbers is 192.

Conclusion

Thus, using the relation between HCF, LCM and the product of two numbers, we find that the required LCM is 192.