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
Here are the HCF and LCM for the given numbers. 1. (i) 24 and 40 Step 1: Find the prime factorization of each number. 24 = 2 × 2 × 2 × 3 = 2^3 × 3^1 40 = 2 × 2 × 2 × 5 = 2^3 × 5^1 Step 2: Calculate the HCF. The HCF is the product of the common prime factors raised to the lowest power. Common prime factor is 2. The lowest power of 2 is 2^3. HCF(24, 40) = 2^3 = 8 Step 3: Calculate the LCM. The LCM is the product of all prime factors (common and non-common) raised to the highest power. Prime factors are 2, 3, 5. Highest power of 2 is 2^3, 3 is 3^1, 5 is 5^1. LCM(24, 40) = 2^3 × 3^1 × 5^1 = 8 × 3 × 5 = 120 HCF: 8 LCM: 120 1. (ii) 18, 36 and 75 Step 1: Find the prime factorization of each number. 18 = 2 × 3 × 3 = 2^1 × 3^2 36 = 2 × 2 × 3 × 3 = 2^2 × 3^2 75 = 3 × 5 × 5 = 3^1 × 5^2 Step 2: Calculate the HCF. The HCF is the product of the common prime factors raised to the lowest power. The only common prime factor is 3. The lowest power of 3 is 3^1. HCF(18, 36, 75) = 3^1 = 3 Step 3: Calculate the LCM. The LCM is the product of all prime factors (common and non-common) raised to the highest power. Prime factors are 2, 3, 5. Highest power of 2 is 2^2, 3 is 3^2, 5 is 5^2. LCM(18, 36, 75) = 2^2 × 3^2 × 5^2 = 4 × 9 × 25 = 36 × 25 = 900 HCF: 3 LCM: 900 1. (iii) 20, 40, 60 and 80 Step 1: Find the prime factorization of each number. 20 = 2 × 2 × 5 = 2^2 × 5^1 40 = 2 × 2 × 2 × 5 = 2^3 × 5^1 60 = 2 × 2 × 3 × 5 = 2^2 × 3^1 × 5^1 80 = 2 × 2 × 2 × 2 × 5 = 2^4 × 5^1 Step 2: Calculate the HCF. The HCF is the product of the common prime factors raised to the lowest power. Common prime factors are 2 and 5. The lowest power of 2 is 2^2. The lowest power of 5 is 5^1. HCF(20, 40, 60, 80) = 2^2 × 5^1 = 4 × 5 = 20 Step 3: Calculate the LCM. The LCM is the product of all prime factors (common and non-common) raised to the highest power. Prime factors are 2, 3, 5. Highest power of 2 is 2^4, 3 is 3^1, 5 is 5^1. LCM(20, 40, 60, 80) = 2^4 × 3^1 × 5^1 = 16 × 3 × 5 = 48 × 5 = 240 HCF: 20 LCM: 240 Send me the next one 📸