Find the LCM of 309, 144, 448, 576 with the LCM of Two or More Numbers Calculator. Here we are teaching you two different methods through which you can calculate the LCM of 309, 144, 448, 576. So, keep reading to learn more.
Given numbers are 309,144,448,576
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 309,144,448,576 is 415296.
Find LCM of 309,144,448,576 with Prime Factorization
2 | 309, 144, 448, 576 |
2 | 309, 72, 224, 288 |
2 | 309, 36, 112, 144 |
2 | 309, 18, 56, 72 |
2 | 309, 9, 28, 36 |
2 | 309, 9, 14, 18 |
3 | 309, 9, 7, 9 |
3 | 103, 3, 7, 3 |
103, 1, 7, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 103 x 1 x 7 x 1 = 415296
Therefore, the lowest common multiple of 309,144,448,576 is 415296.
LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
Firstly, we have to find the product of all the numbers.
309 x 144 x 448 x 576 = 11482103808
Then, let us find the GCF of these five numbers. To do so, we have to list down the factors for each number and choose the highest factor that is in all of the lists.
309 : 1, 3, 103, 309
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
448 : 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448
576 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 309,144,448,576, is 1.
Now, the common factors can be found like this.
309:3x 103
144:2x 2x 2x 2x 3x 3
448:2x 2x 2x 2x 2x 2x 7
576:2x 2x 2x 2x 2x 2x 3x 3
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 3x 3x 3 = 27648
Therefore, the value for common factors is 27648.
Now that we have all the elements of the formula, we can plug them in to calculate the LCM.
LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
LCM = 11482103808/(1x27648)
LCM = 11482103808/27648
LCM = 415296
Thus, we can understand that the LCM of 309,144,448,576 is 415296.
Here are some samples of LCM of two or more Numbers calculations.
1. What is the LCM of 309, 144, 448, 576?
Answer: LCM of 309, 144, 448, 576 is 415296.
2. How to calculate the LCM of 309, 144, 448, 576?
The LCM can be found using two methods. You can either use the LCM formula or the prime factorization method to calculate the LCM of 309, 144, 448, 576.
3. What is the LCM formula?
The LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}.