LCM of 6, 9 and 15 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, 9 and 15, 90 is the first(least or smallest) number that is common in the set of multiples of 6, 9 and 15. The LCM is also known as LCD, Least Common Divisor for 6, 9 and 15 is 90. You can read more on LCM for further details.
What is LCM of 6, 9 and 15
The Least Common Multiple or Lowest Common Multiple of 6, 9 and 15 is 90.
How to Find LCM of 6, 9 and 15?
LCM of 6, 9 and 15 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6, 9 and 15 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 6, 9 and 15 can be expressed as;
6 = 2 × 3
9 = 3 × 3
15 = 3 × 5
LCM (6, 9, 15) = 2 × 3 × 3 × 5 = 90
LCM of 6, 9 and 15 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 |
9 |
15 |
|
3 |
3 |
9 |
15 |
|
3 |
1 |
3 |
5 |
|
5 |
1 |
1 |
5 |
|
× |
1 |
1 |
1 |
LCM (6, 9, 15) = 2 × 3 × 3 × 5 = 90
LCM of 6, 9 and 15 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, 9 and 15
|
Multiples of 6 |
Multiples of 9 |
Multiples of 15 |
|
6 |
9 |
15 |
|
12 |
18 |
30 |
|
18 |
27 |
45 |
|
24 |
36 |
60 |
|
30 |
45 |
75 |
|
36 |
54 |
90 |
|
42 |
63 |
105 |
|
48 |
72 |
120 |
|
54 |
81 |
135 |
|
60 |
90 |
150 |
|
66 |
99 |
165 |
|
72 |
108 |
180 |
|
78 |
117 |
195 |
|
84 |
126 |
210 |
|
90 |
135 |
225 |
LCM (6, 9, 15) = 90
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 6, 9 and 15?
Answer: 90 is the smallest number that is divisible by both 6, 9 and 15.
What is the LCM for 3, 6, 9 and 15?
Answer: LCM for 3, 6, 9 and 15 is 90 as 3 is the prime factor of 6, 9 and 15.
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