Factors and Multiples
(Lowest Common Multiple)
Name:
(
)
Worksheet
6
Class:
Points to Note:
To find L.C.M of 3 or more numbers, the method
used is almost the same.
Example:
Find the lowest common multiple of 420, 63 and 126.
Method 1: (Prime Factorisation)
Step 1:
Factorise all numbers into prime factors.
2
420 = 2 × 3 × 7 × 5
32 × 7
63 =
2
126 = 2 × 3 × 7
Page 22
By: Mr Wong Han Ming
Step 2:
Look at all the indiviual prime numbers and select the biggest number
from each group.
2
420 = 2 × 3 × 7 × 5
32 × 7
63 =
2
126 = 2 × 3 × 7
2
420 = 2 × 3 × 7 × 5
32 × 7
63 =
2
126 = 2 × 3 × 7
For the number 2, 22 is biggest
among the group.
For the number 3, 32 is biggest
among the group.
2
420 = 2 × 3 × 7 × 5
32 × 7
63 =
2
126 = 2 × 3 × 7
2
420 = 2 × 3 × 7 × 5
32 × 7
63 =
2
126 = 2 × 3 × 7
For the number 7, there is only one
option, which is 7, so it is
considered the biggest number.
Step 3:
For the number 5, there is only one
option, which is 5, so it is
considered the biggest number.
Multiply the selected numbers to get the L.C.M
2
420 = 2 × 3 × 7 × 5
32 × 7
63 =
2
126 = 2 × 3 × 7
select the biggest number
2
2
L.C.M = 2 × 3 × 7 × 5
= 1 260
Page 23
By: Mr Wong Han Ming
Method 2: (Continuous Division)
Step 1:
Find a prime number that can divide
all numbers.
3 420
140
63
21
126
42
3 420
7 140
20
63
21
3
126
42
6
3 420
7 140
2 20
10
63
21
3
3
126
42
6
3
(For example, 420, 63 and 126 can
be divided by 3 to get 140, 21 and 42)
Step 2:
Repeat step 1 for the next line of numbers.
(For example, 140, 21 and 42 can
be divided by 7 to get 20, 3 and 6)
Step 3:
Repeat step 2 until there is no more
common factor.
Step 4:
If there is a common factor between
TWO numbers, divide the two
numbers by the factor and leave the
rest of the numbers alone.
(For example, 20 and 6 can
be divided by 2 to get 10 and 3)
leave this number alone
Step 5:
Repeat step 4 until there is no more
common factor between two numbers.
3 420
7 140
2 20
3 10
10
63
21
3
3
1
126
42
6
3
1
Step 4:
Multiplying the circled numbers,
we find the L.C.M to be
3 420
7 140
2 20
3 10
10
63
21
3
3
1
126
42
6
3
1
L.C.M = 3 × 7 × 2 × 3 × 10 × 1 × 1
= 1 260
Page 24
By: Mr Wong Han Ming
Practice:
Find the lowest common multiple of the following.
1)
8, 16 and 18
2)
18, 15 and 24
3)
8, 12 and 36
4)
42, 36 and 24
5)
20, 45 and 60
6)
54, 81 and 108
4)
5)
6)
504
180
324
Answers:
1)
2)
3)
144
360
72
Page 25
By: Mr Wong Han Ming