LCM of 6 and 10
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 6 and 10 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 30 as output. Here you can check the answer for Find the LCM of 6 and 10.
What is LCM of 6 and 10
Given Numbers are 6, 10
We can find the LCM of 6, 10 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 6 and 10
Multiples of 6 =6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,
Multiples of 10 =10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,
Now, get the least common multiple of 6, 10 which is 30
So, the LCM of 6, 10 is 30.
Least Common Multiple (LCM) of 6 and 10 with the help of Prime Factorisation
One method for determining the LCM of 6 and 10 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 6's prime factorization:
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 6 are 2,3.
6 = 21×31
And this is 10's prime factorization:
| 2 | 10 |
| 5 | 5 |
| 1 |
Prime factors of 10 are 2,5.
10 = 21×51
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 2,3,5
.21×31×51 = 30
This shows that the LCM of 6 and 10 is 30.
How to Calculate the LCM of 6 and 10 Using Common Multiples
The first step in determining the Least Common Multiple of 6 and 10 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 6 and 10:
Lets look at the first ten multiples of these numbers, 6 and 10:
6,12,18,24,30,36,42,48,54,102 are the first ten multiples of 6.
10,20,30,40,50,60,70,80,90,170 are the first ten multiples of 10.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 6 and 10, for example, are 72, 102, and 160. 30 is the least common multiple since it is the smallest.
6 and 10 have an LCM of 30.
Least Common Multiple of 6 and 10 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 10, than apply into the LCM equation.
GCF(6,10) = 2
LCM(6,10) = ( 6 × 10) / 2
LCM(6,10) = 60 / 2
LCM(6,10) = 30
Related Least Common Multiples of 6
Related Least Common Multiples of 10
Frequently Asked Questions on LCM of 6 and 10
1. What is the LCM of 6 and 10?
The LCM of 6 and 10 is 30.
2. How to find the lowest common multiple of 6 and 10?
To find the lowest common multiple of 6 and 10, we have to get the multip;es of both numbers and identify the least common multiple in them which is 30.
3. What are the Factors of 6?
Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.
4. What are the Factors of 10?
Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.
5. How to Find the LCM of 6 and 10?Answer:
Least Common Multiple of 6 and 10 = 30
Step 1: Find the prime factorization of 6
6 = 2 x 3
Step 2: Find the prime factorization of 10
10 = 2 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 30 = 2 x 3 x 5
Step 4: Therefore, the least common multiple of 6 and 10 is 30.