LCM of 264 and 272
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 264 and 272 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 8976 as output. Here you can check the answer for Find the LCM of 264 and 272.
What is LCM of 264 and 272
Given Numbers are 264, 272
We can find the LCM of 264, 272 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 264 and 272
Multiples of 264 =264,528,792,1056,1320,1584,1848,2112,2376,2640,2904,3168,3432,3696,3960,4224,4488,
Multiples of 272 =272,544,816,1088,1360,1632,1904,2176,2448,2720,2992,3264,3536,3808,4080,4352,4624,
Now, get the least common multiple of 264, 272 which is 8976
So, the LCM of 264, 272 is 8976.
Least Common Multiple (LCM) of 264 and 272 with the help of Prime Factorisation
One method for determining the LCM of 264 and 272 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 272's prime factorization:
| 2 | 272 |
| 2 | 136 |
| 2 | 68 |
| 2 | 34 |
| 17 | 17 |
| 1 |
Prime factors of 272 are 2,17.
272 = 24×171
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, 3,11,17
.24×31×111×171 = 8976
This shows that the LCM of 264 and 272 is 8976.
How to Calculate the LCM of 264 and 272 Using Common Multiples
The first step in determining the Least Common Multiple of 264 and 272 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 264 and 272:
Lets look at the first ten multiples of these numbers, 264 and 272:
264,528,792,1056,1320,1584,1848,2112,2376,4488 are the first ten multiples of 264.
272,544,816,1088,1360,1632,1904,2176,2448,4624 are the first ten multiples of 272.
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 272, for example, are 3168, 4488, and 4352. 8976 is the least common multiple since it is the smallest.
264 and 272 have an LCM of 8976.
Least Common Multiple of 264 and 272 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 272, than apply into the LCM equation.
GCF(264,272) = 8
LCM(264,272) = ( 264 × 272) / 8
LCM(264,272) = 71808 / 8
LCM(264,272) = 8976
Related Least Common Multiples of 264
Related Least Common Multiples of 272
Frequently Asked Questions on LCM of 264 and 272
1. What is the LCM of 264 and 272?
The LCM of 264 and 272 is 8976.
2. How to find the lowest common multiple of 264 and 272?
To find the lowest common multiple of 264 and 272, we have to get the multip;es of both numbers and identify the least common multiple in them which is 8976.
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 272?
Answer: Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272. There are 10 integers that are factors of 272. The greatest factor of 272 is 272.
5. How to Find the LCM of 264 and 272?Answer:
Least Common Multiple of 264 and 272 = 8976
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 272
272 = 2 x 2 x 2 x 2 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 = 8976 = 2 x 2 x 2 x 2 x 3 x 11 x 17
Step 4: Therefore, the least common multiple of 264 and 272 is 8976.