Fird the LCM and HCF of 1250 and 105

To find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 1250 and 105, we can follow these steps: 1. Find the prime factorization of both numbers. 2. Identify the common prime factors and their powers. 3. Calculate the LCM by multiplying all the prime factors with their highest powers. 4. Calculate the HCF by multiplying all the common prime factors with their lowest powers. Let's start by finding the prime factorization of 1250 and 105: 1. Prime factorization of 1250: \( 1250 = 2 \times 625 \) \( 625 = 5^4 \) So, \( 1250 = 2 \times 5^4 \) 2. Prime factorization of 105: \( 105 = 3 \times 35 \) \( 35 = 5 \times 7 \) So, \( 105 = 3 \times 5 \times 7 \) Now, we can identify the common prime factors and their powers: - The common prime factor is 5. - The power of 5 in 1250 is 4. - The power of 5 in 105 is 1. Next, we calculate the LCM and HCF: LCM = \( 2 \times 5^4 \times 3 \times 7 \) HCF = \( 5^1 \) Let's calculate the LCM and HCF. Calculate the value by following steps: - step0: Calculate: \(2\times 5^{4}\times 3\times 7\) - step1: Multiply the terms: \(42\times 5^{4}\) - step2: Evaluate the power: \(42\times 625\) - step3: Multiply: \(26250\) Calculate or simplify the expression \( 5^1 \). Calculate the value by following steps: - step0: Calculate: \(5^{1}\) - step1: Evaluate the power: \(5\) The LCM of 1250 and 105 is 26250, and the HCF is 5.