LCM of 6, 8 and 9 is 72. LCM often used for Least Common Multiple or the Lowest common multiple, also known as LCD, Least Common Divisor is the number that is a common multiple to the given set of numbers. Here the given set of numbers are 6, 8 and 9. The smallest common multiple for all these numbers among many is 72, and hence it is the LCM. You can refer to LCM for all details.
What is LCM of 6, 8 and 9
The Least Common Multiple or Lowest Common Multiple of 6, 8 and 9 is 72.
How to Find LCM of 6, 8 and 9?
LCM of 6, 8 and 9 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6, 8 and 9 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 6, 8 and 9 can be expressed as;
6 = 2 × 3
8 = 2 × 2 × 2
9 = 3 × 3
The product of common and uncommon prime factors forms the LCM.
LCM (6, 8 and 9) = 2 × 2 × 2 × 3 × 3 = 72
LCM of 6, 8 and 9 Using Division Method
In the Division Method, the numbers 6, 8 and 9 are divided by common prime factors. The division is continued when there are no common prime factors till the remainders are 1. Product of the prime divisors of 6, 8 and 9 forms the LCM.
|
2 |
6 |
8 |
9 |
|
2 |
3 |
4 |
9 |
|
2 |
3 |
2 |
9 |
|
3 |
3 |
1 |
9 |
|
3 |
1 |
1 |
3 |
|
× |
1 |
1 |
1 |
LCM(6, 8 and 9) = 2 × 2 × 2 × 3 × 3 = 72
LCM of 6, 8 and 9 Using Listing the Multiples
By listing all the multiples of 6, 8 and 9, we can identify the LCM. Below is the list of multiples for 6, 8 and 9
|
Multiples of 6 |
Multiples of 8 |
Multiples of 9 |
|
6 |
8 |
9 |
|
12 |
16 |
18 |
|
18 |
24 |
27 |
|
24 |
32 |
36 |
|
30 |
40 |
45 |
|
36 |
48 |
54 |
|
42 |
56 |
63 |
|
48 |
64 |
72 |
|
54 |
72 |
81 |
|
60 |
80 |
90 |
|
66 |
88 |
99 |
|
72 |
96 |
108 |
LCM (6, 8 and 9) = 72
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 6, 8 and 9?
Answer: 72 is the smallest number that is divisible by 6, 8 and 9.
What is the LCM of 2, 3, 6, 8 and 9?
Answer: LCM of 2, 3, 6, 8 and 9 is 72 as 2 is the factor for 6 and 8 whereas 3 is the factor for 6 and 9.
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