Imagine you have two groups of friends, one with 3 friends and the other with 4 friends. You want to give each friend in both groups the same number of candies, but you want to use all the candies. Multiples are like counting in groups. For the group of 3, the multiples are 3, 6, 9, 12, 15, and so on (because you keep adding 3). For the group of 4, the multiples are 4, 8, 12, 16, 20, and so on (because you keep adding 4) Common Multiples are numbers that appear in both lists of multiples. In our example, 12 is a common multiple because it appears in both lists. So, if you had 12 candies, you could give each friend in both groups 4 candies (because 12 divided by 3 is 4 and 12 divided by 4 is 3). Think of it like this: Multiples are like jumping on a number line, but you always jump the same distance. Common multiples are where both jumpers land on the same number at the same time. Finding the Friends of Numbers: Highest Common Factors and Lowest Common Multiples Imagine you have two groups of friends, each wanting to share cookies. • Group A has 12 cookies. • Group B has 18 cookies. They want to share the cookies so that each friend in each group gets the same number of cookies, with no cookies left over. How can they do that? Highest Common Factor (HCF): • Finding the Friends: Let's find the numbers that can divide both 12 and 18 without leaving a remainder. These are called factors. o Factors of 12: 1, 2, 3, 4, 6, 12 o Factors of 18: 1, 2, 3, 6, 9, 18 • The Biggest Friend: The biggest number that is a factor of both 12 and 18 is 6. This is the Highest Common Factor (HCF). • Sharing Cookies: Group A can divide their 12 cookies into 6 groups of 2 cookies each. Group B can divide their 18 cookies into 6 groups of 3 cookies each. Now, everyone gets the same number of cookies! Lowest Common Multiple (LCM): • Finding the Multiples: Now let's imagine the groups want to arrange their cookies in equal rows. They want to use the same number of cookies in each row for both groups. What's the smallest number of cookies they can use? • The Smallest Number: We need to find the smallest number that is a multiple of both 12 and 18. o Multiples of 12: 12, 24, 36, 48... o Multiples of 18: 18, 36, 54... • The Least Common Multiple: The smallest number that is a multiple of both 12 and 18 is 36. This is the Lowest Common Multiple (LCM). • Arranging Cookies: Group A can arrange their 12 cookies in 3 rows of 4 cookies each. Group B can arrange their 18 cookies in 2 rows of 9 cookies each. Now both groups have the same number of cookies in each row! So, remember: • HCF helps us find the largest number that divides two numbers without leaving a remainder (like sharing cookies). • LCM helps us find the smallest number that is a multiple of two numbers (like arranging cookies in rows).