LCM of 18 and 21 is 126. 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. If you consider 126 or 360 or any multiple that is common to 18 and 21, 126 is the first(least or smallest) number that is common in the set of multiples of 18 and 21. The LCM is also known as LCD, Least Common Divisor for 18 and 21 is 126. You can use HCF and LCM to differentiate between HCF and LCM.
What is LCM of 18 and 21
The Least Common Multiple or Lowest Common Multiple of 18 and 21 is 126.
How to Find LCM of 18 and 21?
LCM of 18 and 21 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 18 and 21 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 18 and 21 can be expressed as;
18 = 2 x 3 x 3
21 = 3 x 7
LCM (18, 21) = 2 x 3 x 3 x 7 = 126
LCM of 18 and 21 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.
|
3 |
18 |
21 |
|
3 |
6 |
7 |
|
2 |
2 |
7 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
LCM (18, 21) = 2 x 3 x 3 x 7 = 126
LCM of 18 and 21 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 18 and 21
|
Multiples of 18 |
Multiples of 21 |
|
18 |
21 |
|
36 |
42 |
|
54 |
63 |
|
72 |
84 |
|
90 |
105 |
|
108 |
126 |
|
126 |
147 |
|
144 |
168 |
LCM (18, 21) = 126
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 18 and 21?
Answer: 126 is the smallest number that is divisible by both 18 and 21.
What is the LCM for 1, 2, 18 and 21?
Answer: LCM for 1, 2, 18 and 21 is 126.
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