Download Name of Lecturer: Mr. J.Agius Course: FCES

Name of Lecturer: Mr. J.Agius
Course: FCES
LESSON 7
Multiples and Common Multiples, HCF and LCM
7.1 Multiples and Common Multiples
Multiples are just all the multiplication tables.
Example:
The first 10 multiples of 3 are 3, 6, 9, 12, 15, 18,
21, 24, 27, and 30.
Write which of these
numbers are:
Multiples of 7
1
2
3
4
5
6
7
8
9
10
Multiples of 9
11
12
13
14
15
16
17
18
19
20
Multiples of 13
21
22
23
24
25
26
27
28
29
30
Common multiples
of 3 and 4
31
32
33
34
35
36
37
38
39
40
Multiples of both
2 and 3
41
42
43
44
45
46
47
48
49
50
Multiples of
both 4 and 5
Common multiples
of 5 and 6
Common multiples
of 3 and 5
Learning Outcome 1 – Numerical Calculations
Not multiples of 2,
3 or 4
Common multiples
of 4 and 8
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Name of Lecturer: Mr. J.Agius
Course: FCES
Mixed Exercise
24
9
18
36
50
11
48
16
25
13
20
21
1
Multiples of 2
2
Multiples of 3
3
Multiples of 4
4
Common multiples of 2 and 3
5
Common multiples of 3 and 4
6
Common multiples of 3 and 7
7
Common multiples of 2 and 5
8
Least common multiple of 3 and 4
9
Least common multiple of 2 and 5
Learning Outcome 1 – Numerical Calculations
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Name of Lecturer: Mr. J.Agius
Course: FCES
Common Multiples
Write a number that
is a multiple of:
1
2, 3 and 13
2
2, 3 and 9
3
2, 9 and 18
4
2, 3, 4 and 5
5
6, 8 and 15
6
12, 15 and 20
7
4, 6 and 9
8
3, 4 and 18
9
2, 3 and 21
10
4, 5, 6 and 10
7.2 Highest Common Factor
When you are asked to mention the Highest Common Factor of two numbers or more,
first you have to name all the factors of each number, then, verify the common factors,
and hence determine the highest common factor. This number, in general is used to
reduce fractions to their lowest term, by using the highest common factor of the
numerator and the denominator.
Example:
The highest common factor of 20 and 15 is:
Factors of 20 = 1, 2, 4, 5, 10, 20
Factors of 15 = 1, 3, 5, 15
The common factors are 1 and 5. So the highest common factor is 5.
Learning Outcome 1 – Numerical Calculations
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Name of Lecturer: Mr. J.Agius
Course: FCES
7.3 Lowest Common Multiple
Here we use the same procedure used in the Highest Common Factor. The lowest
common multiple is used to transform two different fractions with different
denominators, and change them to have same denominator. With this way you can add
and subtract fractions.
Example:
The lowest common multiple of 4 and 5 is:
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, …
Multiples of 5 = 5, 10, 15, 20, 25, …
Here the lowest common multiple of 4 and 5 is 20.
Exercise 1:
Write down the highest common factor of
a)
16 and 26
Ans.________
b)
36 and 45
Ans.________
c)
25 and 50
Ans.________
d)
56 and 84
Ans.________
Exercise 2:
a)
5 and 8
Ans.________
b)
9 and 5
Ans.________
c)
13 and 2
Ans.________
d)
9 and 12
Ans.________
e)
4, 5 and 8
Ans.________
f)
8, 6 and 12
Ans.________
Find the lowest common denominator for each pair of fractions.
1.
2.
Learning Outcome 1 – Numerical Calculations
3.
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Name of Lecturer: Mr. J.Agius
Course: FCES
Story Sums
1. Look at these gears.
A
B
a) A completes 10 turns. How many turns does B complete?
b)
What is the least number of turns that A can complete so that B also completes
an exact number of turns?
c)
B completes 30 turns. On how many occasions will both A and B have been
back in their starting position at the same time?
2. Graham’s three children, Angela, Bob and Cathy visit him on Sunday afternoons.
Angela visits every 2 weeks, Bob visits every 3 weeks and Cathy visits every 4
weeks. All three children visited Graham last Sunday.
How often do
a) Angela and Bob visit on the same day?
b) Angela and Cathy visit on the same day?
c) Bob and Cathy visit on the same day?
Learning Outcome 1 – Numerical Calculations
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Name of Lecturer: Mr. J.Agius
Course: FCES
3. James wants to draw the shapes below.
a) In the list below, fill in the missing cells accordingly:
i)
ii)
Find the Least Common Multiple (LCM) of the number of lines obtained for
shapes D and F.
Find the Highest Common Factor (HCF) of the number of lines obtained for
shapes B and G.
b) From the list above:
i)
arrange the numbers in order of size, smallest first;
ii)
write a prime number;
iii) write down a multiple of 3;
iv) write down a factor of 36.
c)
Write the total number of lines as a product of its prime factors in index form.
(hint: 9 = 3 × 3 = 32 )
Learning Outcome 1 – Numerical Calculations
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Name of Lecturer: Mr. J.Agius
4.
Course: FCES
A rectangular lawn measures 420cm by 240cm. What is the largest sized square tile
that can be used to pave the area without any cutting?
A box measures 12cm by 18cm by 24cm. The box is to be filled with cubes so that no
5. space is left.
What is the length of the side of the largest cube that will do this?
Learning Outcome 1 – Numerical Calculations
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Name of Lecturer: Mr. J.Agius
6.
Course: FCES
Three bells start ringing together. If Bell A rings every 6 minutes, Bell B rings every
15 minutes and Bell C rings every 20 minutes.
a) After how many minutes will Bell A and Bell B ring together?
b) After how many minutes will all bells ring together?
c) Think of another situation where such method can be used.
Learning Outcome 1 – Numerical Calculations
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