Main answer:To find the LCM and HCF of the given numbers, we have to write them in prime factors and then find out the highest common factor and lowest common multiple.Let us write the given numbers in prime factorization form:2^4 x 5^3 x 7^22^2 x 3^5 x 7^22^5 x 5^2 x 7^2Now we can easily find out the LCM and HCF.LCM: 2^5 x 3^5 x 5^3 x 7^2HCF: 2^2 x 5^2 x 7^2Answer in more than 100 words:For the given numbers, LCM is 2^5 x 3^5 x 5^3 x 7^2. The LCM is calculated by taking the highest powers of all the factors involved. The given numbers contain the factors 2, 3, 5, and 7. So, the LCM can be calculated by taking the highest powers of these factors. Therefore, LCM of 2^4 x 5^3 x 7^2, 2^2 x 3^5 x 7^2, and 2^5 x 5^2 x 7^2 is 2^5 x 3^5 x 5^3 x 7^2.For the given numbers, HCF is 2^2 x 5^2 x 7^2. The HCF is calculated by taking the smallest powers of all the factors involved. Therefore, HCF of 2^4 x 5^3 x 7^2, 2^2 x 3^5 x 7^2, and 2^5 x 5^2 x 7^2 is 2^2 x 5^2 x 7^2.Conclusion:The LCM of the given numbers is 2^5 x 3^5 x 5^3 x 7^2 and the HCF of the given numbers is 2^2 x 5^2 x 7^2.