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. You've already asked for the prime factorization of 48 and 60. Now, let's find their LCM and GCD using those prime factors. 1. b) Hence, find the LCM and GCD of 48 and 60. Step 1: Recall the prime factorizations of 48 and 60 from the previous step. 48 = 2^4 × 3^1 60 = 2^2 × 3^1 × 5^1 Step 2: Find the Greatest Common Divisor (GCD). To find the GCD, take the lowest power of each common prime factor. The 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). To find the LCM, take the highest power of all prime factors present in either number. The prime factors are 2, 3, and 5. 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 = 240 The GCD of 48 and 60 is 12 and the LCM is 240. What's next?