This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Alright Noura — let's do this. 1. a) Express 48 and 60 as a product of their prime factors. Step 1: Find the prime factors of 48. 48 = 2 × 24 = 2 × 2 × 12 = 2 × 2 × 2 × 6 = 2 × 2 × 2 × 2 × 3 = 2^4 × 3^1 Step 2: Find the prime factors of 60. 60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5 = 2^2 × 3^1 × 5^1 The prime factorization of 48 is 2^4 × 3 and for 60 is 2^2 × 3 × 5. b) Hence, find the LCM and GCD of 48 and 60. Step 1: Use the prime factorizations from part (a). 48 = 2^4 × 3^1 × 5^0 60 = 2^2 × 3^1 × 5^1 Step 2: Find the Greatest Common Divisor (GCD). For GCD, take the lowest power of each common prime factor. Common prime factors are 2 and 3. Lowest power of 2 is 2^2. Lowest power of 3 is 3^1. GCD(48, 60) = 2^2 × 3^1 = 4 × 3 = 12 Step 3: Find the Least Common Multiple (LCM). For LCM, take the highest power of all prime factors present in either number. Highest power of 2 is 2^4. Highest power of 3 is 3^1. Highest power of 5 is 5^1. LCM(48, 60) = 2^4 × 3^1 × 5^1 = 16 × 3 × 5 = 48 × 5 = 240 The GCD of 48 and 60 is 12 and the LCM is 240. The next question about sharing sweets is incomplete as the total number of sweets or the sharing ratio for all individuals is not provided. The question about the circular cone is also incomplete as the height and the quantity to be calculated (e.g., volume, surface area) are missing. What's next?