LCM of 6, 7 and 8 is 168. LCM stands for Least Common Multiple or the Lowest common multiple also known as LCD Least Common Divisor is the positive number that is a common multiple for the given group of numbers. Here the given set of numbers are 6, 7 and 8. The smallest common multiple for all these numbers among many is 168, and hence it is the LCM. You can refer to LCM with Examples to understand better.
What is LCM of 6, 7 and 8
The Least Common Multiple or Lowest Common Multiple of 6, 7 and 8 is 168.
How to Find LCM of 6, 7 and 8?
LCM of 6, 7 and 8 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6, 7 and 8 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 6, 7 and 8 can be expressed as;
6 = 2 × 3
7 = 1 × 7
8 = 2 × 2 × 2
The product of prime factors of 6, 7 and 8 forms the LCM. Therefore
LCM(6, 7 and 8) = 2 × 2 × 2 × 3 × 7 = 168
LCM of 6, 7 and 8 Using Division Method
In the Division Method, following steps are followed
- Divide the number 6, 7 and 8 by prime numbers starting from the smallest.
- All numbers to be divided till the remainder is 1.
- Multiply the prime divisors to get the LCM.
Division table for 6, 7 and 8 shown below;
|
2 |
6 |
7 |
8 |
|
2 |
3 |
7 |
4 |
|
2 |
3 |
7 |
2 |
|
3 |
3 |
7 |
1 |
|
7 |
1 |
7 |
1 |
|
× |
1 |
1 |
1 |
LCM(6, 7 and 8) = 2 × 2 × 2 × 3 × 7 = 168
LCM of 6, 7 and 8 Using Listing the Multiples
By listing all the multiples of 6, 7, and 8, we can observe the smallest/least common multiple, which is the LCM. Below is the list of multiples for 6, 7 and 8
Multiples of 6
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180
Multiples of 7
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182
Multiples of 8
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184
LCM(6, 7 and 8) = 168
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 6, 7 and 8?
Answer: 168 is the smallest number that is divisible by 6, 7 and 8.
What is the LCM of 3 and 168?
Answer: LCM of 3 and 168 is 168.
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