Multiples
Group Activity 17
In pairs:
- List the first ten counting numbers.
- Take any of the counting numbers.
- Multiply the number taken by each of the ten counting numbers.
- List the products obtained.
- Discuss and share the results with other groups.
Note
Each of the products obtained is a multiple of the number you took.
Example 17
Find the first five multiples of 12.
Multiples of 12 are 12 × 1, 12 × 2, 12 × 3, 12 × 4 and 12 × 5.
These are 12, 24, 36, 48 and 60.
Exercise T
T1
In pairs, write the first ten multiples of 8.
T2
Write the first eight multiples of 15.
T3
Write the first five multiples of:
- 18
- 24
- 12
- 26
- 32
- 42
- 56
- 60
- 76
- 84
T5
List all the multiples of 4 between 42 and 70.
- 48
- 54
- 68
- 96
- 102
- 144
Common multiples
Group Activity 18
In groups of three:
- List the first eight multiples of 3.
- List the first eight multiples of 4.
- Identify the multiples of 3 that are also multiples of 4.
- Discuss the results and share with other groups.
Note
The multiples of 3 that are also multiples of 4 are the common multiples.
Example 18
Find the first three common multiples of 4 and 6.
- Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32 and 36.
- Multiples of 6 are 6, 12 , 18, 24, 30, 36 and 42.
- Common multiples of 4 and 6 are:
12, 24 and 36.
Exercise U
- 2 and 5
, - 3 and 8
, - 2, 3 and 4
,
U2
In pairs, find the first four common multiples of 3, 4 and 6.
U3
Find the first three common multiples of 5 and 6.
U4
Kuti packs mangoes in either groups of 5 or 6. Which of the following number of mangoes can be packed into such groups without any mangoes remaining?
45, 60, 72, 0, 120 and 200.
Least common multiples
Group Activity 19
In groups of three:
- List the first five multiples of 4.
- List the first five multiples of 6.
- Identify and write the common multiples of 4 and 6.
- Identify the least (smallest) of the common multiples of 4 and 6.
- Discuss the results and share with other groups.
Note
The smallest of the common multiples is the least common multiple (LCM) of the numbers.
Example 19
Find the LCM of 2 and 3.
- Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.
- Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24.
- Common multiples of 2 and 3 are:
6, 12, 18, 24 …. - LCM is 6.
Exercise V
- 3 and 5
LCM is . - 2, 3 and 4
LCM is .
V2
Find the LCM of 2 and 9.
V3
Find the LCM of 12 and 15.
V4
Find the LCM of 8 and 12.
V5
Find the least number that is divisible by 3 and 7.
V6
Find the least number of apples that can be shared equally among 3 or 4 people.
V7
A tailor makes suits that require either 3 metres or 4 metres of cloth. Find the smallest length of cloth she would buy to make suits of both sizes without any cloth remaining.
V8
An electrician required pieces of wire of either 12 metres or 16 metres long. Find the length of the shortest wire that can be cut into equal pieces of both length.
V9
A security light flashes after every 6 minutes. Another security light flashes after every 5 minutes. The two lights were switched on and flashed together the same time. Find, after how long the two lights flashed together again?