This document discusses highest common factors (HCF) and lowest common multiples (LCM). It defines multiples as numbers divisible by another with no remainder. Common multiples contain each number a number of times. The lowest common multiple is the smallest number divisible by all numbers. To find the LCM, list multiples and find the lowest number common to all lists. Similarly, factors divide a number with no remainder, and the highest common factor is the largest number dividing all numbers. The document provides examples of finding HCF and LCM.

1. Highest Common FactorsHighest Common Factors
& Lowest common& Lowest common
MultiplesMultiples

2. MultiplesMultiples
 What is a multiple?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?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

3. Lowest Common MultiplesLowest Common Multiples
 What do we mean by ‘lowestWhat do we mean by ‘lowest
common multiple’?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 commonHow can we find lowest common
multiples?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

4. Finding Lowest common multiplesFinding Lowest common multiples
 Example:Example:
Find the lowest common multiple of 3
and 7..
First few multiples of 3:
3 6 9 12 15 18 21
First few multiples of 7:
7 14 21
The lowest common multiple of 3 and 7 is:
2121

5. LOWEST COMMON MULTIPLESLOWEST 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 = 30 LCM = 24

6. FactorsFactors
 What is a factor?What is a factor?
Factors of a number are those numbers that
divide into it exactly with no remainder.
*What are common factors?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.

7. Highest Common FactorsHighest Common Factors
 What do we mean by highestWhat do we mean by highest
common factor?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 commonHow can we find highest common
factors?factors?
List the first few factors of each number
Look for the highest number that appears
in all lists.

8. Finding Highest CommonFinding Highest Common
FactorsFactors
 ExampleExample
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
33

9. Highest common factorsHighest common factors
 Find the highest common factors ofFind the highest common factors of
the following sets of numbers.the following sets of numbers.
20 and 30
HCF = 10
14 and 12
HCF = 2
24, 36, and 42
HCF = 6
40, 45 and 50
HCF = 5

10. Prime FactorsPrime Factors
 Sometimes we want to find just theSometimes we want to find just the
prime factors of two numbers.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