Difference Between GCF and LCM

GCF vs LCM

GCF and LCM are two important concepts that are taught in junior mathematics classes. These are important concepts in mathematics that are used even in later classes to solve bigger, tougher questions which makes it imperative to understand what these two terms mean and what the difference between these two are.

GCF

Also called the Greatest Common factor, it refers to the greatest factor that two or more numbers have in common. It is the product of all the prime factors these numbers have in common. Let us see this by an example.

16= 2x2x2x2

24=2x2x2x3

There are three 2’s common to both the numbers, hence the GCF would be 2x2x2=8

LCM

To understand Lowest Common Multiple, we need to know what multiples are. It is a number that is a multiple of 2 or more numbers. For example, if 2 and 3 are the numbers given to us, 0, 6, 12, 18, 24…. are the multiples of these two numbers.

It is clear then that Least Common Multiple is the smallest number (excluding zero) that is a multiple of the two numbers. In this example of course it is 6.

LCM is also known as the smallest integer that can be divided by both the given numbers. Here,

6/2=3

And 6/3=2.

As 6 is divisible by both 2 and 3, it is the LCM of 2 and 3.

The difference between GCF and LCM is self explanatory. While GCF is the largest number shared between the factors of two or more numbers, LCM is the smallest number that is divisible by both (or more) the numbers. To find either the LCM or the GCF of 2 or more numbers, it is necessary to factorize them.