LCM of 2, 3, 4, 5 and 6 is 60. LCM or least common multiple is the simplest method to find out the smallest common multiples between two or more than two numbers.
Here the LCM of 2,3,4,5 and 6 is the smallest positive integer 60 that is divisible by 2,3,4,5 and 6 where there is no remainder.
What is LCM of 2,3,4,5 and 6
The Least Common Multiple or Lowest Common Multiple of 2,3,4,5 and 6 is 60.
How to Find LCM of 2,3,4,5 and 6?
LCM of 2,3,4,5 and 6 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 2,3,4,5 and 6 Using Prime Factorisation Method
Let us find the LCM of 2,3,4,5 and 6 by the Prime factorization method stepwise :
Step 1: Find all the prime factors of numbers 2, 3, 4, 5 and 6
Step 2: Now, list down all the prime numbers found,
Prime factorisation of 2,3,4,5 and 6 are as follows:
2: 21
3: 31
4: 22
5: 51
6: 21× 31
Step 3: LCM of 2, 3, 4, 5 and 6 can be obtained by multiplying prime factors raised to their highest power.
Hence, the LCM of 2, 3, 4, 5 and 6 by prime factorization is = 22 × 31× 51 = 60.
LCM of 2, 3, 4, 5 and 6 by division method
To Calculate the LCM of 2, 3, 4, 5 and 6
Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2, 3, 4, 5 and 6.
Step 2: If any of the numbers either 2, 3, 4,5 and 6 is a multiple of 2, divide it by 2 and write the quotient below it. If any number is not divisible by the prime number then bring it below.
Step 3: Continue this process until you get only 1s in the last row.
The LCM of 2, 3, 4, 5 and 6 by division method = 2 × 2 × 3 × 5 = 60.
| 2 | 2 | 3 | 4 | 5 | 6 |
| 2 | 1 | 3 | 2 | 5 | 3 |
| 3 | 1 | 3 | 1 | 5 | 3 |
| 5 | 1 | 1 | 1 | 5 | 1 |
| 1 | 1 | 1 | 1 | 1 |
LCM of 2,3,4,5 and 6 by Listing Multiples
First, to find the LCM of 2, 3, 4, 5 and 6, first, list the multiples of 2, 3, 4, 5 and 6
2 – 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ..
3 – 3, 6, 9, 12, 15, 18, 21, 24, 27, 30..
4 – 4, 8, 12, 16, 20, 24, 28, 32, 36…
5 – 5, 10, 15, 20, 25, 30, 35, 40..
6 – 6, 12, 18, 24, 30, 36,42, 48…
Step 1: List out a few multiples of 2, 3, 4, 5 and 6 as shown above
Step 2: Now the common multiples from the multiples of 2, 3, 4, 5 and 6 are 60, 120…
Step 3: The smallest common multiple of 2,3,4,5 and 6 is 60.
Hence the least common multiple of 2,3,4,5 and 6 = 60
Related Articles
Video Lesson on Applications of LCM
Solved Example
Example:
What is the smallest number that is divisible by 2, 3, 4, 5 and 6 exactly?
Solution:
The smallest number that is divisible by 2,3,4,5 and 6 exactly is their LCM.
Therefore, the LCM of 2, 3, 4, 5 and 6 is 60.
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