Highest Common Factors & Lowest common Multiples 9Y4 Tuesday 30 th November 2004

Multiples  What is a multiple? A number that may be divided by another number with no remainder: 4, 6, and 12 are multiples of 2. i.e. Multiples of 3 are all those numbers which appear in the 3 times table  What are common multiples? A common multiple of two or more numbers contains each of them a number of times exactly, so, 24 is a common multiple of 3 and 4. i.e. A number which appears in the times tables of all the numbers you are considering

Lowest Common Multiples  What do we mean by ‘lowest common multiple’? The smallest multiple that is exactly divisible by every member of a set of numbers. i.e. the lowest common multiple of 12 and 18 is 36  How can we find lowest common multiples? Write out the first few multiples of all the numbers in the data set Look for the lowest number that appears in all the lists

Finding Lowest common multiples  Example:. Find the lowest common multiple of 3 and 7. First few multiples of 3: First few multiples of 7: The lowest common multiple of 3 and 7 is: 21

LOWEST COMMON MULTIPLES Find the lowest common multiples for the following sets of numbers: 5 and 7 6 and 10 4, 6, and 12 LCM = 35 LCM = 30LCM = 24

Factors  What is a factor? Factors of a number are those numbers that divide into it exactly with no remainder. * What are common factors? I.e. the factors of 12 are 1, 12, 2, 6, 3 and 4. Common factors are those factors which divide exactly into all the numbers in the set.

Highest Common Factors  What do we mean by highest common factor? The highest common factor of a data set is the largest number that divides exactly into all the numbers. *How can we find highest common factors? List the first few factors of each number Look for the highest number that appears in all lists.

Finding Highest Common Factors  Example Find the highest common factor of 12 and 15. The factors of 12 are: 1, 2, 3, 4, 6, and 12 The factors of 15 are: 1, 3, 5, 15 So the highest common factor of 12 and 15 is 3

Highest common factors  Find the highest common factors of the following sets of numbers. 20 and 30 HCF = and 12 HCF = 2 24, 36, and 42 HCF = 6 40, 45 and 50 HCF = 5

Prime Factors  Sometimes we want to find just the prime factors of two numbers. What is a prime number? A prime number only has 2 factors and those 2 factors must be 1 and the number itself. The first 5 prime numbers are: 2, 3, 5, 7, and 11