 Hello and welcome to this session. Let us understand the following question today. Find the LCM and HCF of the following pairs of integers and verify that LCM multiplied by HCF is equal to the product of the two numbers. We have 510 and 92. Now before writing the solution, let us understand what is HCF and LCM. HCF is equal to product of the smallest part of each common prime factor in the numbers and LCM is equal to product of the greatest part of each prime factor involved in the numbers. This is the key idea behind our question. Now let us understand the solution. Given to us are two numbers 510 and 92. 510 can be written as 2 multiplied by 3 multiplied by 5 multiplied by 17 and 92 can be written as 2 multiplied by 2 multiplied by 23 or 2 squared multiplied by 23. Therefore, my key idea HCF is equal to 2 and LCM is equal to 2 squared multiplied by 3 multiplied by 5 multiplied by 17 multiplied by 23 which is equal to 23460. Now let's verify. We have to verify that LCM multiplied by HCF is equal to product of the two numbers. Now let us consider left hand side. LCM multiplied by HCF is equal to 23460 multiplied by 2 which is equal to 46920. Now let us consider the RHS product of the given two numbers is equal to 510 multiplied by 92 which is equal to 46920. Therefore, LHS is equal to RHS hence verified. Therefore, the required answer is HCF is equal to 2 and LCM is equal to 23460. I hope you understood this question. Bye and have a nice day.