LCM of 300 and 306
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 300 and 306 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 15300 as output. Here you can check the answer for Find the LCM of 300 and 306.
What is LCM of 300 and 306
Given Numbers are 300, 306
We can find the LCM of 300, 306 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 300 and 306
Multiples of 300 =300,600,900,1200,1500,1800,2100,2400,2700,3000,3300,3600,3900,4200,4500,4800,5100,
Multiples of 306 =306,612,918,1224,1530,1836,2142,2448,2754,3060,3366,3672,3978,4284,4590,4896,5202,
Now, get the least common multiple of 300, 306 which is 15300
So, the LCM of 300, 306 is 15300.
Least Common Multiple (LCM) of 300 and 306 with the help of Prime Factorisation
One method for determining the LCM of 300 and 306 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 300's prime factorization:
| 2 | 300 |
| 2 | 150 |
| 3 | 75 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 300 are 2, 3,5.
300 = 22×31×52
And this is 306's prime factorization:
| 2 | 306 |
| 3 | 153 |
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 306 are 2, 3,17.
306 = 21×32×171
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, 3,5,17
.22×32×52×171 = 15300
This shows that the LCM of 300 and 306 is 15300.
How to Calculate the LCM of 300 and 306 Using Common Multiples
The first step in determining the Least Common Multiple of 300 and 306 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 300 and 306:
Lets look at the first ten multiples of these numbers, 300 and 306:
300,600,900,1200,1500,1800,2100,2400,2700,5100 are the first ten multiples of 300.
306,612,918,1224,1530,1836,2142,2448,2754,5202 are the first ten multiples of 306.
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 300 and 306, for example, are 3600, 5100, and 4896. 15300 is the least common multiple since it is the smallest.
300 and 306 have an LCM of 15300.
Least Common Multiple of 300 and 306 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 300 and 306, than apply into the LCM equation.
GCF(300,306) = 6
LCM(300,306) = ( 300 × 306) / 6
LCM(300,306) = 91800 / 6
LCM(300,306) = 15300
Related Least Common Multiples of 300
Related Least Common Multiples of 306
Frequently Asked Questions on LCM of 300 and 306
1. What is the LCM of 300 and 306?
The LCM of 300 and 306 is 15300.
2. How to find the lowest common multiple of 300 and 306?
To find the lowest common multiple of 300 and 306, we have to get the multip;es of both numbers and identify the least common multiple in them which is 15300.
3. What are the Factors of 300?
Answer: Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300. There are 18 integers that are factors of 300. The greatest factor of 300 is 300.
4. What are the Factors of 306?
Answer: Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. There are 12 integers that are factors of 306. The greatest factor of 306 is 306.
5. How to Find the LCM of 300 and 306?Answer:
Least Common Multiple of 300 and 306 = 15300
Step 1: Find the prime factorization of 300
300 = 2 x 2 x 3 x 5 x 5
Step 2: Find the prime factorization of 306
306 = 2 x 3 x 3 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 15300 = 2 x 2 x 3 x 3 x 5 x 5 x 17
Step 4: Therefore, the least common multiple of 300 and 306 is 15300.