LCM of 8 and 9 is 72. LCM, also known as Least Common multiple or Lowest common multiple, is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 8 and 9, 72 is the least number that is divisible by both 8 and 9. 144 is also the common multiple of 8 and 9, however it is not the smallest common multiple. Therefore the LCM or LCD also known as the Least Common divisor for 8 and 9 is 72. You can use the Prime Factorization and Division method to find the LCM of given numbers.
What is LCM of 8 and 9
The Least Common Multiple or Lowest Common Multiple of 8 and 9 is 72.
How to Find LCM of 8 and 9?
LCM of 8 and 9 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8 and 9 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 8 and 9 can be expressed as;
8 = 2 x 2 x 2
9 = 3 x 3
LCM (8, 9) = 2 x 2 x 2 x 3 x 3 = 72
LCM of 8 and 9 Using Division Method
In the Division Method, the given set of numbers are written in the same row separated by a comma. These numbers are divided with the smallest number that divides all until no further division is possible;
|
2 |
8 |
9 |
|
2 |
4 |
9 |
|
2 |
2 |
9 |
|
3 |
1 |
9 |
|
3 |
1 |
3 |
|
x |
1 |
1 |
Hence, LCM (8, 9) = 2 x 2 x 2 x 3 x 3 = 72
LCM of 8 and 9 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 8 and 9
|
Multiples of 8 |
Multiples of 9 |
|
8 |
9 |
|
16 |
18 |
|
24 |
27 |
|
32 |
36 |
|
40 |
45 |
|
48 |
54 |
|
56 |
63 |
|
64 |
72 |
|
72 |
81 |
|
80 |
90 |
LCM (8, 9) = 72
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 8 and 9?
Answer: 72 is the smallest number that is divisible by both 8 and 9.
What is the LCM for 1, 8 and 9?
Answer: 72 is the LCM for 1, 8 and 9.
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