LCM of 305 and 309
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 305 and 309 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 94245 as output. Here you can check the answer for Find the LCM of 305 and 309.
What is LCM of 305 and 309
Given Numbers are 305, 309
We can find the LCM of 305, 309 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 305 and 309
Multiples of 305 =305,610,915,1220,1525,1830,2135,2440,2745,3050,3355,3660,3965,4270,4575,4880,5185,
Multiples of 309 =309,618,927,1236,1545,1854,2163,2472,2781,3090,3399,3708,4017,4326,4635,4944,5253,
Now, get the least common multiple of 305, 309 which is 94245
So, the LCM of 305, 309 is 94245.
Least Common Multiple (LCM) of 305 and 309 with the help of Prime Factorisation
One method for determining the LCM of 305 and 309 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 305's prime factorization:
| 5 | 305 |
| 61 | 61 |
| 1 |
Prime factors of 305 are 5,61.
305 = 51×611
And this is 309's prime factorization:
| 3 | 309 |
| 103 | 103 |
| 1 |
Prime factors of 309 are 3,103.
309 = 31×1031
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: 5,61, 3,103
.31×51×611×1031 = 94245
This shows that the LCM of 305 and 309 is 94245.
How to Calculate the LCM of 305 and 309 Using Common Multiples
The first step in determining the Least Common Multiple of 305 and 309 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 305 and 309:
Lets look at the first ten multiples of these numbers, 305 and 309:
305,610,915,1220,1525,1830,2135,2440,2745,5185 are the first ten multiples of 305.
309,618,927,1236,1545,1854,2163,2472,2781,5253 are the first ten multiples of 309.
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 305 and 309, for example, are 3660, 5185, and 4944. 94245 is the least common multiple since it is the smallest.
305 and 309 have an LCM of 94245.
Least Common Multiple of 305 and 309 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 305 and 309, than apply into the LCM equation.
GCF(305,309) = 1
LCM(305,309) = ( 305 × 309) / 1
LCM(305,309) = 94245 / 1
LCM(305,309) = 94245
Related Least Common Multiples of 305
Related Least Common Multiples of 309
Frequently Asked Questions on LCM of 305 and 309
1. What is the LCM of 305 and 309?
The LCM of 305 and 309 is 94245.
2. How to find the lowest common multiple of 305 and 309?
To find the lowest common multiple of 305 and 309, we have to get the multip;es of both numbers and identify the least common multiple in them which is 94245.
3. What are the Factors of 305?
Answer: Factors of 305 are 1, 5, 61, 305. There are 4 integers that are factors of 305. The greatest factor of 305 is 305.
4. What are the Factors of 309?
Answer: Factors of 309 are 1, 3, 103, 309. There are 4 integers that are factors of 309. The greatest factor of 309 is 309.
5. How to Find the LCM of 305 and 309?Answer:
Least Common Multiple of 305 and 309 = 94245
Step 1: Find the prime factorization of 305
305 = 5 x 61
Step 2: Find the prime factorization of 309
309 = 3 x 103
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 94245 = 3 x 5 x 61 x 103
Step 4: Therefore, the least common multiple of 305 and 309 is 94245.