#### Solved Examples and Worksheet for Least Common Multiples of Whole Numbers

Q1Find the LCM of 3 and 5.

A. 35
B. 8
C. 2
D. 15

Step: 1
Write the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27
and multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45
Step: 2
Since the least common multiple of 3 and 5 is 15, the LCM of 3 and 5 is 15
[Select the least common multiple.]
Q2Find the LCM of 3 and 7.

A. 21
B. 10
C. 27
D. 35

Step: 1
Write the multiples of 3 and 7 and select the least multiple the numbers have in common.
Step: 2
The LCM of 3 and 7 is 21.
Q3Chris plays football every 3rd day and Justin plays every 2nd day in a week. When will they both play together in the week?

A. 2
B. 6
C. 3
D. 5

Step: 1
The LCM of 2 and 3 would be the day on which they play together.
Step: 2
List the multiples of 2 and 3 and circle the lowest number in common.
Step: 3
Both Chris and Justin play football together on 6th day.
Q4Find the LCM of 18 and 45 using a Venn diagram.

A. 90
B. 18
C. 45
D. 63

Step: 1
18 = 1 x 2 x 3 x 3
45 = 1 x 3 x 3 x 5
[Write the prime factors for 18 and 45.]
Step: 2
Represent all the prime factors of 18 and 45 in a Venn diagram.
Step: 3
2 x 3 x 3 x 5 = 90
[Multiply all the factors in the Venn diagram.]
Step: 4
The LCM of 18 and 45 is 90.
Q5Channel-A repeatedly broadcasts news for 40 minutes, channel-B repeatedly for 60 minutes and Channel-C repeatedly for 80 minutes. If all the channels start broadcasting news now, then after how many minutes will they broadcast news at the same time?
A. Three channels will never be administered together.
B. 200 minutes
C. 180 minutes
D. 240 minutes
E. 160 minutes

Step: 1
All the three channels will be broadcast together at the common multiples of the time intervals.
Step: 2
L.C.M of 40, 60 and 80 = 240.
Step: 3
For every 240 minutes, the three channels broadcast news at the same time.
Correct Answer is :   240 minutes
Q6Find the LCM of 15 and 25.
A. 40
B. 25
C. 75
D. 35

Step: 1
Write the multiples of 15 and 25 and circle the lowest number in common.
Step: 2
The LCM of 15 and 25 is 75.
Q7Find the LCM of 20 and 25.

A. 200
B. 175
C. 250
D. 100

Step: 1
Write the multiples of 20 and 25 and select the lowest multiple the numbers have in common.
Step: 2
The LCM of 20 and 25 is 100.
Q8Find the LCM of 4, 8 and 16.
A. 48
B. 32
C. 96
D. 16

Step: 1
[Write the multiples of 4, 8 and 16 and select the lowest number in common.]

Step: 2
So, the LCM of 4, 8 and 16 is 16.
Q9Find the LCM of 12 and 18.
A. 36
B. 22
C. 18

Step: 1
Write the multiples of 12 and 18 and circle the lowest number in common.
Step: 2
The LCM of 12 and 18 is 36.
Q10Find the least common multiple of 5 and 8.
A. 44
B. 4
C. 40
D. 14

Step: 1
The smallest common multiple of two or more numbers is called lowest common multiple (LCM).
Step: 2
Write the multiples of 5 and 8.
Step: 3
Choose the smallest multiple from their common multiples, which is 40.
Step: 4
The LCM of 5 and 8 is 40.
Q11Find the LCM of 9 and 12.
A. 88
B. 60
C. 70
D. 36

Step: 1
Write the multiples of 9 and 12
Step: 2
Select the lowest multiple the numbers have in common.
Step: 3
The LCM of 9 and 12 is 36.
Q12Find the LCM of 12 and 16.
A. 90
B. 48
C. 100
D. 96

Step: 1
The smallest common multiple of two or more numbers is called lowest common multiple (LCM).
Step: 2
List the multiples of 12 and 16.
Step: 3
Choose the smallest multiple from their common multiples, which is 48.
Step: 4
Hence, the LCM of 12 and 16 is 48.
Q13Find the LCM of 10, 20 and 30.
A. 15
B. 90
C. 10
D. 60

Step: 1
The smallest common multiple of two or more numbers is called lowest common multiple (LCM).
Step: 2
List the multiples of 10, 20 and 30.
Step: 3
Choose the smallest multiple from their common multiples, which is 60.
Step: 4
Hence, the LCM of 10, 20 and 30 is 60.
Q14Find the LCM of 2, 3 and 4.
A. 15
B. 50
C. 12
D. 75

Step: 1
The smallest common multiple of two or more numbers is called lowest common multiple (LCM).
Step: 2
List the multiples of 2, 3 and 4.
Step: 3
Choose the smallest multiple from their common multiples, which is 12.
Step: 4
Hence the LCM of 2, 3 and 4 is 12.