LCM of 7, 8 and 9 is 504. Least Common Multiple or the Lowest common multiple often referred to as LCM is the first multiple in the common set of multiples of any 2 or more numbers. It is also known as LCD, Least Common Divisor. Here the given set of numbers are 7, 8 and 9. The smallest common multiple for all these numbers among many is 504, and hence it is the LCM. You can refer to LCM with Examples to understand better.
What is LCM of 7, 8 and 9
The Least Common Multiple or Lowest Common Multiple of 7, 8 and 9 is 504.
How to Find LCM of 7, 8 and 9?
LCM of 7, 8 and 9 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 7, 8 and 9 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 7, 8 and 9 can be expressed as;
7 = 1 × 7
8 = 2 × 2 × 2
9 = 3 × 3
All the prime factors of 7, Prime factors of 8 and prime factors of 9 are multiplied to get the LCM.
Therefore, LCM(7, 8 and 9) = 2 × 2 × 2 × 3 × 3 × 7 = 504
LCM of 7, 8 and 9 Using Division Method
In the Division Method, 7, 8 and 9 divided by prime divisors starting with 2. Once the division is completed using prime divisors in increasing order, their product forms the LCM.
|
2 |
7 |
8 |
9 |
|
2 |
7 |
4 |
9 |
|
2 |
7 |
2 |
9 |
|
3 |
7 |
1 |
9 |
|
3 |
7 |
1 |
3 |
|
7 |
7 |
1 |
1 |
|
× |
1 |
1 |
1 |
Therefore, LCM(7, 8 and 9) = 2 × 2 × 2 × 3 × 3 × 7 = 504
LCM of 7, 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 7, 8 and 9
Multiples of 7
7, 14, 21, 28, …., 98, 105, 112, 119, 126, …, 175, 182, 189, 196, … 231, 238, 245, 252, …, 308, 315, 322, 329, …., 371, 378, 385, 392, …, 434, 441, 448, 455, … 490, 497, 504, 511, 518
Multiples of 8
8, 16, 24, 32, 40, … 112, 120, 128, …, 168, 176, 184, 192, …, 248, 256, 264, 272, …, 336, 344, 352, 360, …., 432, 440, 448, 456, …, 496, 504, 512, 520
Multiples of 9
9, 18, 27, 36, 45, …, 135, 144, 153, 162, 171, …. 225, 234, 243, 252, …, 306, 315, 324, 333, …, 387, 396, 405, 414, …, 477, 486, 495, 504, 513, 522
LCM(7, 8 and 9) = 504
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 7, 8 and 9?
Answer: 504 is the smallest number that is divisible by 7, 8 and 9.
What is the LCM of 3, 7 and 504?
Answer: LCM of 3, 7 and 504 is 504.
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