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![[Maths] Do you see that, in each case, the number by which the LCM is - Property Involving both the HCF and the LCM](https://cdn.teachoo.com/ef920c19-5165-47a0-a8a2-cb562f1f8e70/slide68.jpg)
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 January 23, 2026 by Teachoo
Property Involving both the HCF and the LCM
Class 7 (Ganita Prakash 1, 2 & old NCERT)
Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)
- The Greatest of All
- Prime Factorisation
- Finding HCF using Prime Factorisation
- Figure it out - Page 54
- Least, but not Last!
- Finding LCM using Prime Factorisation
- Patterns, Properties, and a Pretty Procedure!
- Figure it out - Page 59
- Miscellenaous Questions on HCF, LCM
- Efficient Procedures for HCF and LCM
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Property Involving both the HCF and the LCM
- Figure it out - Page 63, 64
Transcript
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!
