LCM of 264 and 268
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 264 and 268 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 17688 as output. Here you can check the answer for Find the LCM of 264 and 268.
What is LCM of 264 and 268
Given Numbers are 264, 268
We can find the LCM of 264, 268 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 264 and 268
Multiples of 264 =264,528,792,1056,1320,1584,1848,2112,2376,2640,2904,3168,3432,3696,3960,4224,4488,
Multiples of 268 =268,536,804,1072,1340,1608,1876,2144,2412,2680,2948,3216,3484,3752,4020,4288,4556,
Now, get the least common multiple of 264, 268 which is 17688
So, the LCM of 264, 268 is 17688.
Least Common Multiple (LCM) of 264 and 268 with the help of Prime Factorisation
One method for determining the LCM of 264 and 268 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 264's prime factorization:
| 2 | 264 |
| 2 | 132 |
| 2 | 66 |
| 3 | 33 |
| 11 | 11 |
| 1 |
Prime factors of 264 are 2, 3,11.
264 = 23×31×111
And this is 268's prime factorization:
| 2 | 268 |
| 2 | 134 |
| 67 | 67 |
| 1 |
Prime factors of 268 are 2,67.
268 = 22×671
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, 3,11,67
.23×31×111×671 = 17688
This shows that the LCM of 264 and 268 is 17688.
How to Calculate the LCM of 264 and 268 Using Common Multiples
The first step in determining the Least Common Multiple of 264 and 268 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 264 and 268:
Lets look at the first ten multiples of these numbers, 264 and 268:
264,528,792,1056,1320,1584,1848,2112,2376,4488 are the first ten multiples of 264.
268,536,804,1072,1340,1608,1876,2144,2412,4556 are the first ten multiples of 268.
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 264 and 268, for example, are 3168, 4488, and 4288. 17688 is the least common multiple since it is the smallest.
264 and 268 have an LCM of 17688.
Least Common Multiple of 264 and 268 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 264 and 268, than apply into the LCM equation.
GCF(264,268) = 4
LCM(264,268) = ( 264 × 268) / 4
LCM(264,268) = 70752 / 4
LCM(264,268) = 17688
Related Least Common Multiples of 264
Related Least Common Multiples of 268
Frequently Asked Questions on LCM of 264 and 268
1. What is the LCM of 264 and 268?
The LCM of 264 and 268 is 17688.
2. How to find the lowest common multiple of 264 and 268?
To find the lowest common multiple of 264 and 268, we have to get the multip;es of both numbers and identify the least common multiple in them which is 17688.
3. What are the Factors of 264?
Answer: Factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264. There are 16 integers that are factors of 264. The greatest factor of 264 is 264.
4. What are the Factors of 268?
Answer: Factors of 268 are 1, 2, 4, 67, 134, 268. There are 6 integers that are factors of 268. The greatest factor of 268 is 268.
5. How to Find the LCM of 264 and 268?Answer:
Least Common Multiple of 264 and 268 = 17688
Step 1: Find the prime factorization of 264
264 = 2 x 2 x 2 x 3 x 11
Step 2: Find the prime factorization of 268
268 = 2 x 2 x 67
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 17688 = 2 x 2 x 2 x 3 x 11 x 67
Step 4: Therefore, the least common multiple of 264 and 268 is 17688.