How to find the HCF and LCM (Two Numbers)

Video 1

To understand what the HCF and LCM is, please make sure you know how to use a Venn diagram and understand what the product of prime factors for a number is. If you do not know, please check the product of prime factors page. This is simple to understand.
We know what the highest common factor is from the factors, prime factors and HCF page. If we have two or more whole numbers and we want to know the highest/biggest common factor between them, then we first express the whole numbers as a product of its prime factors, as shown in the product of prime factors page.

Video 1 Explanation

The LOWEST COMMON MULTIPLE is the lowest/smallest multiple of two or more numbers. In our example in video 1, we had two numbers of which we needed to find the HCF and LCM of, 32 and 16.
To do so first express 32 and 16 as a product of its prime factors.
32 has its own prime factor product which is 2 x 2 x 2 x 2 x 2. These integers form the product, these integers a
16 has its own prime factor product which is 2 x 2 x 2 x 2

What we need to do is sort the elements in the product for each whole number, in our case 36 and 16,into a Venn diagram.
The elements for 32 are 2,2,2,2,2 because 2 x 2 x 2 x 2 x 2 = 32.
The elements for 16 are 2,2,2,2 because 2 x 2 x 2 x 2 = 16
Given we have sorted out the elements, as in video 1, we can see that in the intersection there are four 2's and one 2 in the part of 32's circle which does not include the intersection.
To find the HCF of the two numbers multiply all the elements with each other in the intersection.
In our intersection, we have 2,2,2,2.
So the HCF of 32 and 16 is 2 x 2 x 2 x 2 = 16
To find the lowest common multiple you multiply all the elements together in the two circles.
So all the elements in the circle are the 2,2,2,2,2
So the LCM of 32 and 16 is 2 x 2 x 2 x 2 x 2 = 32

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