 Hello and welcome to the session. Let us understand the following question today. Find the LCM and HCF of the following integers by applying the Trimfactorization method. We have 12, 15 and 21. Now let's write the solution. Given to us the three numbers are 12, 15 and 21. Here we know 12 can be written as 2 multiplied by 2 multiplied by 3 or 2 square multiplied by 3 and 15 can be written as 3 multiplied by 5 and 21 can be written as 3 multiplied by 7. Therefore HCF is equal to the common term that is 3. Now let's find the LCM. For finding the LCM we have to do the prime factorization. So we have 12, 15 and 21. So here we can see that 2 is the least number by which we have to divide these three numbers. So dividing the three numbers by 2 we get 6, 16 as it is and 21 as it is as both of them are not divisible by 2. So now again it can be divided by 2 because 6 is divisible by 2. So dividing it by 2 we get 3 and 15 and 21 alters because again they are not divisible by 2. Now we can see that 3 is the least number which can be divided by them. So dividing the three numbers by 3 we get 1, dividing 15 by 3 we get 5, dividing 21 by 3 we get 7. Now it is clear that it can be further divided by 5, 1 as it is 1 and 7. Now finally we are left with 7 and 7 is the prime number so dividing it by 7 we get 1, 1 and 1. Therefore required LCM is equal to 2 multiplied by 2 multiplied by 3 multiplied by 5 multiplied by 7. 2 multiplied by 2 is 4 multiplied by 3 multiplied by 5 multiplied by 7. Which is equal to 12 multiplied by 35 which is equal to 420. Hence the required LCM is equal to 420 and HCF is equal to 3. I hope you understood this question. Bye and have a nice day.