Prime factorisation is a method used to find the highest common factor (HCF) of two or more numbers. It involves breaking down each number into its prime factors and then finding the common factors among them. The process is typically done in separate tables for each number.


1. Start by listing the prime factors of each number in separate tables.
2. To find the prime factors, divide the number by the smallest prime number (2) and continue dividing until you cannot divide any further.
3. Repeat this process for each number, listing their prime factors in separate tables.


Once the prime factorisation of each number is obtained, we can find the HCF by identifying the common factors. These are the prime factors that appear in all the tables.


In contrast to HCF, prime factorisation in the context of finding the least common multiple (LCM) involves combining the prime factors of all the numbers into a single table. The purpose is to determine the smallest number that is divisible by all the given numbers.


1. Begin by listing the prime factors of each number in a single table.
2. To find the prime factors, divide each number by the smallest prime number (2) and continue dividing until you cannot divide any further.
3. Combine all the prime factors obtained from each number into a single table.


After obtaining the combined table of prime factors, we can find the LCM by multiplying all the prime factors together. Each prime factor should be taken the maximum number of times it appears in the table.


The reason for using separate tables in HCF is to compare the prime factors of each number individually and identify the common factors among them. This allows us to find the highest common factor.

In LCM, however, the objective is to find the least common multiple, which is obtained by combining all the prime factors of the given numbers into a single table. This approach ensures that the resulting number is divisible by all the given numbers.

Using separate tables in HCF helps in finding the common factors efficiently, while combining the prime factors in LCM simplifies the process of finding the least common multiple. Both methods are tailored to the specific goal of either finding the highest common factor or the least common multiple, respectively.