LCM of 21 and 22 is 462. The Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 21 and 22, 462 is the first(least or smallest) number that is common in the set of multiples of 21 and 22. 168 is also the common multiple of 21 and 462. However, 462 is the smallest. Hence 462 is the LCM which is also known as LCD, Least Common Divisor for 21 and 22. You can read more on LCM for further details.
What is LCM of 21 and 22
The Least Common Multiple or Lowest Common Multiple of 21 and 22 is 462.
How to Find LCM of 21 and 22?
LCM of 21 and 22 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 21 and 22 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 21 and 22 can be expressed as;
21 = 3 x 7
22 = 2 x 11
LCM (21, 22) = 2 x 3 x 7 x 11 = 462
LCM of 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 |
21 |
22 |
|
2 |
3 |
22 |
|
3 |
3 |
11 |
|
11 |
1 |
11 |
|
x |
1 |
1 |
Hence, LCM (21, 22) = 2 x 3 x 7 x 11 = 462
LCM of 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 21 and 22
Multiples of 21:
21, 42, 63, 84, … 189, 210…. 231, 252… 273, 294…. 378, 399….441, 462, 483, ….
Multiples of 22:
22, 44, 66, …. 198, 220, … 308, 330, … 418, 440, 462, 484…
LCM (21, 22) = 462
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 21 and 22?
Answer: 462 is the smallest number that is divisible by both 21 and 22.
What is the LCM for 7, 21 and 22?
Answer: LCM for 7, 21 and 22 is 462.
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