LCM of 306 and 310
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 306 and 310 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 47430 as output. Here you can check the answer for Find the LCM of 306 and 310.
What is LCM of 306 and 310
Given Numbers are 306, 310
We can find the LCM of 306, 310 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 306 and 310
Multiples of 306 =306,612,918,1224,1530,1836,2142,2448,2754,3060,3366,3672,3978,4284,4590,4896,5202,
Multiples of 310 =310,620,930,1240,1550,1860,2170,2480,2790,3100,3410,3720,4030,4340,4650,4960,5270,
Now, get the least common multiple of 306, 310 which is 47430
So, the LCM of 306, 310 is 47430.
Least Common Multiple (LCM) of 306 and 310 with the help of Prime Factorisation
One method for determining the LCM of 306 and 310 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 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
And this is 310's prime factorization:
| 2 | 310 |
| 5 | 155 |
| 31 | 31 |
| 1 |
Prime factors of 310 are 2, 5,31.
310 = 21×51×311
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, 3,17, 5,31
.21×32×51×171×311 = 47430
This shows that the LCM of 306 and 310 is 47430.
How to Calculate the LCM of 306 and 310 Using Common Multiples
The first step in determining the Least Common Multiple of 306 and 310 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 306 and 310:
Lets look at the first ten multiples of these numbers, 306 and 310:
306,612,918,1224,1530,1836,2142,2448,2754,5202 are the first ten multiples of 306.
310,620,930,1240,1550,1860,2170,2480,2790,5270 are the first ten multiples of 310.
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 306 and 310, for example, are 3672, 5202, and 4960. 47430 is the least common multiple since it is the smallest.
306 and 310 have an LCM of 47430.
Least Common Multiple of 306 and 310 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 306 and 310, than apply into the LCM equation.
GCF(306,310) = 2
LCM(306,310) = ( 306 × 310) / 2
LCM(306,310) = 94860 / 2
LCM(306,310) = 47430
Related Least Common Multiples of 306
Related Least Common Multiples of 310
Frequently Asked Questions on LCM of 306 and 310
1. What is the LCM of 306 and 310?
The LCM of 306 and 310 is 47430.
2. How to find the lowest common multiple of 306 and 310?
To find the lowest common multiple of 306 and 310, we have to get the multip;es of both numbers and identify the least common multiple in them which is 47430.
3. 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.
4. What are the Factors of 310?
Answer: Factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310. There are 8 integers that are factors of 310. The greatest factor of 310 is 310.
5. How to Find the LCM of 306 and 310?Answer:
Least Common Multiple of 306 and 310 = 47430
Step 1: Find the prime factorization of 306
306 = 2 x 3 x 3 x 17
Step 2: Find the prime factorization of 310
310 = 2 x 5 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 47430 = 2 x 3 x 3 x 5 x 17 x 31
Step 4: Therefore, the least common multiple of 306 and 310 is 47430.