Determining LCM and HCF with prime factors

How can you determine the LCM of two large numbers such as 36 and 225? With the help of those numbers’ prime factors. When you determine the product of the prime factors of 36 as 22 x 32 and the product of the prime factors of 225 as 32 x 52, you can determine the LCM. How? The LCM of those two numbers (36 and 225) is the product of the highest power of each prime factor, namely 22 x 32 x 52 and that is 900. In other words, when you write the multiples of 36 and the multiples of 225, the first overlapping multiple will be 900.

When determining the HCF on the other hand, you take the lowest power of each common prime factor of the two numbers. In the example of the numbers 36 and 225, the common prime factor is 3 and the lowest power is 32 and that gives you a HCF of 9.