Question 3 - Figure it out - Page 63, 64 - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

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Question 3 (a) Find the HCF and LCM of the following (state your answers in the form of prime factorisations): 3 × 3 × 5 × 7 × 7 and 12 × 7 × 11Writing both numbers in Prime Factorisation form First number = 3 × 3 × 5 × 7 × 7 And, Second number = 12 × 7 × 11 = 2 × 2 × 3 × 7 × 11 Now, putting one below the other First number = 3 × 3 × 5 × 7 × 7 Second number = 2 × 2 × 3 × 7 × 11 Thus, HCF = 3 × 7 = 21 Finding LCM Since there are 2 numbers We use the property Product of numbers = HCF × LCM (3 × 3 × 5 × 7 × 7) × (2 × 2 × 3 × 7 × 11) = 21 × LCM 21 × LCM = (3 × 3 × 5 × 7 × 7) × (2 × 2 × 3 × 7 × 11) LCM = 𝟏/𝟐𝟏 × (3 × 3 × 5 × 7 × 7) × (2 × 2 × 3 × 7 × 11) LCM = (3 × 5 × 7) × (2 × 2 × 3 × 7 × 11) LCM = 2 × 2 × 3 × 3 × 5 × 7 × 7 × 11 LCM = 22 × 32 × 5 × 72 × 11 LCM = 97,020 Question 3 (b) Find the HCF and LCM of the following (state your answers in the form of prime factorisations): 45 and 36Using Shortcut Method Thus, HCF = 3 × 3 = 9 LCM = (3 × 3) × (5 × 4) = 9 × 20 = 180