LCM of 2, 4, 6, 8 and 10 is 120. Least Common multiple or Lowest common multiple, which is used as LCM as a short form, is the smallest and least positive numeral that is divisible by the given set of numbers. Consider the example for finding the LCM of 2, 4, 6, 8 and 10. The answer is 120. 120 is the first number that is commonly divisible by 2, 4, 6, 8 and 10. One can use the Prime Factorization and Division method to find the LCM for the given set of numbers.
What is LCM of 2, 4, 6, 8 and 10
The Least Common Multiple or Lowest Common Multiple of 2, 4, 6, 8 and 10 is 120.
How to Find LCM of 2, 4, 6, 8 and 10?
LCM of 2, 4, 6, 8 and 10 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 2, 4, 6, 8 and 10 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 2, 4, 6, 8 and 10 are expressed as ;
2 = 1 × 2
4 = 2 × 2
6 = 2 × 3
8 = 2 × 2 × 2
10 = 2 × 5
Consolidating all the prime numbers and their products forms the LCM.
Therefore, LCM (2, 4, 6, 8, 10) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 2, 4, 6, 8 and 10 Using Division Method
The Division Method follows the following steps;
- First we need to divide the numbers 2, 4, 6, 8 and 10. As they are all even numbers start with 2
- If no further division is possible for even a single number, use the next prime factor3.
- Complete the division by increasing the prime factors and till the remainder for all numbers remain as 1.
- Product of the prime divisors forms the LCM.
|
2 |
2 |
4 |
6 |
8 |
10 |
|
2 |
1 |
2 |
3 |
4 |
5 |
|
2 |
1 |
1 |
3 |
2 |
5 |
|
3 |
1 |
1 |
3 |
1 |
5 |
|
5 |
1 |
1 |
1 |
1 |
5 |
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× |
1 |
1 |
1 |
1 |
1 |
Therefore LCM (2, 4, 6, 8, 10) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 2, 4, 6, 8 and 10 Using Listing the Multiples
By listing all the multiples 2, 4, 6, 8 and 10, we can easily pick the smallest common multiple, which is the LCM.
Multiples of 2
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124
Multiples of 4
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128
Multiples of 6
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132
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
LCM (2, 4, 6, 8, 10) = 120
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 2, 4, 6, 8 and 10?
Answer: 120 is the smallest number that is divisible by 2, 4, 6, 8 and 10.
What is the LCM of 8 and 120?
Answer: LCM of 8 and 120 is 120.
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