LCM of 310, 288, 510, 578
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 310, 288, 510, 578 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 310, 288, 510, 578. So, keep reading to learn more.
Given numbers are 310,288,510,578
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 310,288,510,578 is 12900960.
Find LCM of 310,288,510,578 with Prime Factorization
| 2 | 310, 288, 510, 578 |
| 3 | 155, 144, 255, 289 |
| 5 | 155, 48, 85, 289 |
| 17 | 31, 48, 17, 289 |
| 31, 48, 1, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 17 x 31 x 48 x 1 x 17 = 12900960
Therefore, the lowest common multiple of 310,288,510,578 is 12900960.
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.
310 x 288 x 510 x 578 = 26317958400
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.
310 : 1, 2, 5, 10, 31, 62, 155, 310
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
510 : 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
578 : 1, 2, 17, 34, 289, 578
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 310,288,510,578, is 2.
Now, the common factors can be found like this.
310:2x 5x 31
288:2x 2x 2x 2x 2x 3x 3
510:2x 3x 5x 17
578:2x 17x 17
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 3x 5x 17 = 1020
Therefore, the value for common factors is 1020.
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 = 26317958400/(2x1020)
LCM = 26317958400/2040
LCM = 12900960
Thus, we can understand that the LCM of 310,288,510,578 is 12900960.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 310, 288, 510, 578
1. What is the LCM of 310, 288, 510, 578?
Answer: LCM of 310, 288, 510, 578 is 12900960.
2. How to calculate the LCM of 310, 288, 510, 578?
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 310, 288, 510, 578.
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}.