LCM of 300, 585, 490, 720
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 300, 585, 490, 720 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 300, 585, 490, 720. So, keep reading to learn more.
Given numbers are 300,585,490,720
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 300,585,490,720 is 2293200.
Find LCM of 300,585,490,720 with Prime Factorization
| 2 | 300, 585, 490, 720 |
| 2 | 150, 585, 245, 360 |
| 3 | 75, 585, 245, 180 |
| 3 | 25, 195, 245, 60 |
| 5 | 25, 65, 245, 20 |
| 5, 13, 49, 4 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 5 x 13 x 49 x 4 = 2293200
Therefore, the lowest common multiple of 300,585,490,720 is 2293200.
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.
300 x 585 x 490 x 720 = 61916400000
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.
300 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
585 : 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585
490 : 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490
720 : 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
5 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 300,585,490,720, is 5.
Now, the common factors can be found like this.
300:2x 2x 3x 5x 5
585:3x 3x 5x 13
490:2x 5x 7x 7
720:2x 2x 2x 2x 3x 3x 5
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 3x 3x 3x 5x 5 = 5400
Therefore, the value for common factors is 5400.
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 = 61916400000/(5x5400)
LCM = 61916400000/27000
LCM = 2293200
Thus, we can understand that the LCM of 300,585,490,720 is 2293200.
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FAQs on LCM of 300, 585, 490, 720
1. What is the LCM of 300, 585, 490, 720?
Answer: LCM of 300, 585, 490, 720 is 2293200.
2. How to calculate the LCM of 300, 585, 490, 720?
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 300, 585, 490, 720.
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}.