LCM of 8, 10 and 15 is 120. LCM is the full form for Least Common Multiple. It can also be the Lowest Common Multiple. The other term is LCD which is Least Common Divisor. LCM/LCD is the positive number that is a common multiple to the given lot of numbers. Here the given numbers are 8, 10 and 15. The smallest common multiple for all these numbers among many is 120, and hence it is the LCM. You can refer to LCM with Examples to understand better.
What is LCM of 8, 10 and 15
The Least Common Multiple or Lowest Common Multiple of 8, 10 and 15 is 120.
How to Find LCM of 8, 10 and 15?
LCM of 8, 10 and 15 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8, 10 and 15 Using Prime Factorisation Method
In the Prime Factorisation method,
- Express the numbers as factors of prime numbers
- Identify the common factors
- Product of the common factors, forms the LCM. Here, 8, 10 and 15 can be expressed as;
8 = 2 × 2 × 2
10 = 2 × 5
15 = 3 × 5
LCM(8, 10 and 15) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 8, 10 and 15 Using Division Method
In the Division Method, the given set of numbers are divided by prime numbers. The numbers are divided starting with the smallest prime factor. The division should be completed till the remainder becomes 1. The product of the prime factors become the LCM.
|
2 |
8 |
10 |
15 |
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2 |
4 |
5 |
15 |
|
2 |
2 |
5 |
15 |
|
3 |
1 |
5 |
15 |
|
5 |
1 |
5 |
5 |
|
× |
1 |
1 |
1 |
LCM(8, 10 and 15) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 8, 10 and 15 Using Listing the Multiples
By listing all the multiples it becomes easy to identify the common multiple that is also the smallest.
Multiples of 8:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136
Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140
Multiples of 15:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150
LCM(8, 10 and 15) = 120
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 8, 10 and 15?
Answer: 120 is the smallest number that is divisible by 8, 10 and 15.
What is the LCM of 15 and 120?
Answer: LCM of 15 and 120 is 120 as 15 is a factor of 120.
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