Question 1 - Page 63 - Property Involving both the HCF and the LCM - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

Last updated at August 10, 2026 by

[Maths] Do you see that, in each case, the number by which the LCM is - Property Involving both the HCF and the LCM

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Question 1 - Page 63 Do you see that, in each case, the number by which the LCM is multiplied to get the product is actually the HCF? Thus, our observations seem to suggest the following: HCF × LCM = Product of the two numbers. Why does this happen? Can you give an explanation or proof? The product of two numbers contains all the factors of both numbers combined. The HCF counts the common factors once. The LCM counts the common factors once AND the unique factors. When you multiply HCF × LCM, you are essentially multiplying (Common Factors) × (All Factors). This is exactly the same as multiplying the two original numbers!

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