LCM of 8, 12 and 20 is 120. Least Common Multiple or the Lowest common multiple is always abbreviated as LCM. It is also known as LCD, Least Common Divisor. LCM/LCD is the positive integer that is a common multiple to the given set of numbers. Here the given set of numbers are 8, 12 and 20. 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, 12 and 20
The Least Common Multiple or Lowest Common Multiple of 8, 12 and 20 is 120.
How to Find LCM of 8, 12 and 20?
LCM of 8, 12 and 20 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8, 12 and 20 Using Prime Factorisation Method
In the Prime Factorisation method, 8, 12 and 20 can be expressed as;
8 = 2 × 2 × 2
12 = 2 × 2 × 3
20 = 2 × 2 × 5
For LCM, the factors of 8, factor 3 from 12 and 5 from 20 is considered. Product of these numbers forms the LCM.
LCM(8, 12 and 20) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 8, 12 and 20 Using Division Method
Follow the mentioned steps for the Division Method,
- 8, 12 and 20 are divided by prime numbers starting from 2 and greatest prime factors that divides any given number.
- Once the remainders of all numbers is 1, multiply the prime divisors, which becomes the LCM.
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2 |
8 |
12 |
20 |
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2 |
4 |
6 |
10 |
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2 |
2 |
3 |
5 |
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3 |
1 |
3 |
5 |
|
5 |
1 |
1 |
5 |
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× |
1 |
1 |
1 |
LCM(8, 12 and 20) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 8, 12 and 20 Using Listing the Multiples
By listing all the multiples of 8, 12 and 20, we can verify the smallest common multiple, which is the LCM. Below is the list of multiples for 8, 12 and 20
Multiples of 8:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136
Multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144
Multiples of 20:
20, 40, 60, 80, 100, 120, 140, 160
LCM(8, 12 and 20) = 120
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 8, 12 and 20?
Answer: 120 is the smallest number that is divisible by 8, 12 and 20.
What is the LCM of 8 and 120?
Answer: LCM of 8 and 120 is 120, as 8 is a factor of 120.
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