Question 1 - Page 62 - Property Involving both the HCF and the LCM - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

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Question 1(a) - Page 62 Explore whether the LCM is a factor of the product in the following cases. If yes, identify the number that the LCM should be multiplied by to get the product. Do you see any pattern? Use these numbers: (a) 45, 105Using Shortcut Method Thus, HCF = 5 × 3 = 15 LCM = (5 × 3) × (3 × 7) = 15 × 21 = 315 Now, Product of two numbers = 45 × 105 = 4725 And, HCF × LCM = 15 × 315 = 4725 So, we can write Product of two Numbers = LCM × HCF Question 1(b) - Page 62 Explore whether the LCM is a factor of the product in the following cases. If yes, identify the number that the LCM should be multiplied by to get the product. Do you see any pattern? Use these numbers: (b) 275, 352Using Shortcut Method Thus, HCF = 11 LCM = (11) × (25 × 32) = 8800 Now, Product of two numbers = 275 × 352 = 96,800 And, HCF × LCM = 11 × 8800 = 96,800 So, we can write Product of two Numbers = LCM × HCF Question 1(c) - Page 62 Explore whether the LCM is a factor of the product in the following cases. If yes, identify the number that the LCM should be multiplied by to get the product. Do you see any pattern? Use these numbers: (c) 222, 370Using Shortcut Method Thus, HCF = 2 × 37 = 74 LCM = (2 × 37) × (3 × 5) = 74 × 15 = 1110 Now, Product of two numbers = 222 × 370 = 82,140 And, HCF × LCM = 74 × 1110 = 82,140 So, we can write Product of two Numbers = LCM × HCF