LCM of 7, 11, 21 and 22 is 462. LCM stands for Least Common Multiple or the Lowest common multiple also known as LCD Least Common Divisor is the positive integer that is a common multiple to the given set of numbers. Here the given set of numbers are 7,11,21 and 22. The smallest common multiple for all these numbers among many is 462, and hence it is the LCM.
You can refer to the LCM page for more details.
What is LCM of 7, 11, 21 and 22
The Least Common Multiple or Lowest Common Multiple of 7, 11, 21 and 22 is 462.
How to Find LCM of 7, 11, 21 and 22?
LCM of 7, 11, 21 and 22 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 7, 11, 21 and 22 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 7, 11, 21 and 22 can be expressed as;
7 = 1 x 7
11 = 1 x 11
21 = 7 x 3
22 = 2 x 11
LCM (7, 11, 21, 22) = 2 x 3 x 7 x 11 = 462
LCM of 7, 11, 21 and 22 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 or only when prime numbers are left.
|
7 |
7 |
11 |
21 |
22 |
|
11 |
1 |
11 |
3 |
22 |
|
2 |
1 |
1 |
3 |
2 |
|
3 |
1 |
1 |
3 |
1 |
|
x |
1 |
1 |
1 |
1 |
Hence, LCM (7,11, 21, 22) = 2 x 3 x 7 x 11 = 462
LCM of 7, 11, 21 and 22 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, 11, 21 and 22
Multiples of 7: 7, 14, 21, …..224, 231…, 420, 427… 462, 469, 476….
Multiples of 11: 11, 22, 33….231, 242.., 357, 378,.. 441, 462, …
Multiples of 21: 21, 42, 63, …., 273, 294, 314…,441, 462,…
Multiples of 22: 22, 44, 66…220, 242, 264,…440, 462,…
LCM (7, 11, 21, 22) = 462
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 7, 11, 21 and 22?
Answer: 462 is the smallest number that is divisible by 7, 11, 21 and 22.
What is the LCM of 7 and 14?
Answer: LCM of 7 and 14 is 14.
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