This document discusses lowest common multiples, factors, highest common factors, and prime numbers. It provides examples of finding the LCM and HCF of various number pairs. It defines a factor as a number that divides evenly into another number. Prime numbers are defined as numbers divisible only by 1 and themselves. Examples are given of listing the prime factors of different numbers.

1. Multiples,Factors and Primes

2. Objectives In this lesson you will get to work on finding lowest common multiples finding Factors of numbers finding highest Common Factors finding Prime numbers

3. Lowest Common Multiple The lowest common multiple(LCM) of 3 and 4 is the lowest number which is in both the 3 and 4 times table. First list out the 3 times tables: 3, 6, 9, 12 ,15, …. Then list out the 4 times table: 4, 8, 12, 16, 20, 24…. The first number which comes up in both is 12. 12 is the most common multiple of 3 and 4.

4. Questions Find the LCM of these number pairs 9 and 6 8 and 12 9 and 15 24 and 18

5. The LCM can help us compare fractions. Example which is bigger 1 / 6 or 3 / 8 ? They are difficult to compare because they have different denominators(the bottom numbers) 1 / 6 3 / 8 Find equivalent fractions which have a common denominator. (same bottom number)

6. To find the common denominator find the LCM of 6 and 8 Multiples of 8 are 8, 16, 24, 32.. Multiples of 6 are 6, 12,18, 24.. The LCM of 6 and 8 is 24 Now convert each fraction into 24ths 1 / 6 x 4 = 4 / 24 3 / 8 x 3 = 9 / 24 By finding a common denominator we can can now compare the fractions and see that 3/8 is bigger

7. What is a factor? A number which divides exactly into another number is called a factor of that number. Here is a way to find the factors of 20 Can 20 be divided by 1 exactly 20 ÷ 1 = 20 20 ÷ 5 = 4 20 ÷ 20 = 1 20 ÷ 4 = 5 20 ÷ 2 = 10 20 ÷ 10 = 2 We already have 5 as a factor. This 20 ÷ 3 = No means we have listed all the factors of. 20 ÷ 4 = 5 20. 1, 2, 4, 5, 10, 20

8. Defination A number which divides exactly unto another number with no remainders is called a factor of that number. List the factors of 16 1, 2, 4, 8, 16 36 1, 2, 3, 4, 6, 9, 12, 18, 36. 100 1, 2, 4, 5, 10, 20, 25, 50, 100

9. Highest Common Factors What is the biggest number that 18 and 30 can be divided into without leaving a remainder List the factors of 18 1, 2, 3, 6, 9, 18 List the factors of 30. 1, 2, 3, 5, 6, 10, 15, 30 The biggest number in both lists is 6. We say that the highest common factor of 18 and 30 is 6.

10. Questions Find the highest common factors of 6 and 15 15 and 50 12 and 66 39 and 52 21 and 36 and 60

11. Prime numbers A prime number is a number that can only be divided by itself and the number 1. Write down the prime numbers up to 20 2, 3, 5, 7, 11, 13, 17, 19

12. Prime Factors Can you list the prime factors of the following numbers. In other words list the factors and circle the ones which are prime numbers 48 1, 2, 3, 4, 6, 8, 12, 16, 24, 28 25 1, 5, 25 17 1, 17