HCF and LCM Explained with Easy Animations

Today we'll explore how to find the Highest Common Factor of numbers.To understand factors, let's look at different ways we can arrange twelve blocks.So the factors of twelve are one, two, three, four, six, and twelve.Now let's find the factors of eighteen using the same method.The factors of eighteen are one, two, three, six, nine, and eighteen.Let's compare the factors of twelve and eighteen to find their common factors.Let's see how HCF helps us share candies equally. We have twelve yellow candies and eighteen pink candies.Since six is the highest common factor, we can share these candies equally among six children. Each child will get two yellow candies and three pink candies.To find the least common multiple, let's first understand what multiples are.Let's look at the multiples of 4. We can find them by counting up by fours.Now let's find the multiples of 6 in the same way.Let's identify the numbers that are multiples of both 4 and 6. These are called common multiples.The smallest number in our list of common multiples is 12. This is called the Least Common Multiple, or LCM, of 4 and 6.Now that we understand HCF and LCM separately, let's explore their fascinating relationship.Let's use our example numbers 12 and 18 to demonstrate this relationship.We can visualize this relationship using an area model. The rectangle's dimensions represent our numbers.The area of this rectangle can be calculated in two ways: either by multiplying 12 and 18 directly, or by multiplying their HCF and LCM.Let's look at the factors of both numbers to understand why this relationship works.The common factors between 12 and 18 are 1, 2, 3, and 6, with 6 being the HCF.Now, let's see when to use HCF versus LCM in practical situations.We use HCF when we need to divide things equally, like sharing cookies and candies among children.LCM is used when we need to find when cycles align, like determining when different timed tasks will coincide.On this timeline, we can see when the 12-minute and 18-minute tasks align at their LCM of 36 minutes.Remember, the product of our original numbers equals the product of their HCF and LCM.