Transcript HCM-LCFv2

Puzzle
Can you draw this without going over the same
line twice and without taking your pen off the
page?
Multiples, factors and primes
To revise the definitions of multiples factors and
primes
To understand the meanings of HCF and LCM
To learn an algorithm to computes the HCF and LCM
Recap- multiples
Write down the first five multiples of:
a) 3
a)3, 6, 9, 12, 15
b)5
b)5, 10, 15, 20, 25, 30
c) 4
c)4, 8, 12, 16, 20
d)11
d)11, 22, 33, 44, 55
e)9
e)9, 18, 27, 36, 45
Definition
• Product – An answer to a
multiplication problem.
7 x 8 = 56
Product
Definition
•
Factor – a number that divides into
another number WITHOUT a remainder
7 x 8 = 56
Factors – because 56 ÷ 8 = 7
What are the other factors of
56?
1, 2, 4, 7, 8, 14, 38, 56
Definition
• Prime Number – a number that has
exactly two factors, itself and 1.
What are the first ten prime
numbers?
2, 3, 5, 7, 11, 13, 17, 19, 23, 27
Prime factor decomposition
Write the number 36 as the product of its
prime factors
36
2
18
2
36 = 2 x 2 x 3 x 3
36 = 22 x 32
9
3
3
Prime factor decomposition
Write the number 28 as the product of its
prime factors
28
7
4
2
28 = 2 x 2 x 7
28 = 22 x 7
2
Prime factor decomposition
HCF and LCM
HCF is Highest Common Factor
The HCF of 18 and 24 is…
6
LCM is Lowest Common Multiple
The LCM of 12 and 15 is…
60
Find the HCF and LCM
of 24 and 60
1. Use a factor tree to help you find
the Prime Factors
2.Then a Venn Diagram to help you
find the HCF and LCM
FACTOR TREES
24
4
2
60
6
22
4
3
2
15
2 3
5
Venn Diagram
HCF is the
region of
intersection
2 x 2 x 3 = 12
24 = 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
60
24
2
2
2
3
HCF = 2 x 2 x 3 = 12
LCM = 2 x 2 x 2 x 3 x 5 = 120
5
LCM is all the
numbers in the circles
multiplied together
2 x 2 x 2 x 3 x 5=120