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
Hey Noura, good to see you again. To find the LCM and GCD, we first need the prime factorization of 48 and 60. (These were determined in a previous step). Prime factorization of 48 = 2^4 × 3^1 Prime factorization of 60 = 2^2 × 3^1 × 5^1 Step 1: Find the Greatest Common Divisor (GCD). For the GCD, we take the lowest power of each common prime factor. The common prime factors are 2 and 3. The lowest power of 2 is 2^2. The lowest power of 3 is 3^1. GCD(48, 60) = 2^2 × 3^1 = 4 × 3 = 12 Step 2: Find the Least Common Multiple (LCM). For the LCM, we take the highest power of all prime factors present in either number. The highest power of 2 is 2^4. The highest power of 3 is 3^1. The highest power of 5 is 5^1. LCM(48, 60) = 2^4 × 3^1 × 5^1 = 16 × 3 × 5 = 240 The GCD of 48 and 60 is 12 and the LCM is 240. Send me the next one 📸