LCM of 6, 15 and 18 is 90. 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 6, 15 and 18, 90 is the first(least or smallest) number that is common in the set of multiples of 6, 15 and 18. The LCM, also known as LCD, Least Common Divisor for 6, 15 and 18 is 90. You can use the LCM with Examples for better understanding.
What is LCM of 6, 15 and 18
The Least Common Multiple or Lowest Common Multiple of 6, 15 and 18 is 90.
How to Find LCM of 6, 15 and 18?
LCM of 6, 15 and 18 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6, 15 and 18 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 6, 15 and 18 can be expressed as;
6 = 2 × 3
15 = 3 × 5
18 = 2 × 3 × 3
LCM (6, 15, 18) = 2 × 3 × 3 × 5 = 90
LCM of 6, 15 and 18 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.
|
2 |
6 |
15 |
18 |
|
3 |
3 |
15 |
9 |
|
3 |
1 |
5 |
3 |
|
5 |
1 |
5 |
1 |
|
× |
1 |
1 |
1 |
LCM (6, 15, 18) = 2 × 3 × 3 × 5 = 90
LCM of 6, 15 and 18 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 6, 15 and 18
|
Multiples of 6 |
Multiples of 15 |
Multiples of 18 |
|
6 |
15 |
18 |
|
12 |
30 |
36 |
|
18 |
45 |
54 |
|
24 |
60 |
72 |
|
30 |
75 |
90 |
|
36 |
90 |
108 |
|
42 |
105 |
126 |
|
48 |
120 |
144 |
|
54 |
135 |
162 |
|
60 |
150 |
180 |
|
66 |
165 |
198 |
|
72 |
180 |
216 |
|
78 |
195 |
234 |
|
84 |
210 |
252 |
|
90 |
225 |
270 |
LCM (6, 15, 18) = 90
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 6, 15 and 18?
Answer: 90 is the smallest number that is divisible by both 6, 15 and 18.
What is the LCM for 3, 6, 9, 15 and 18?
Answer: LCM for 3, 6, 9, 15 and 18 is 90.
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