LCM of 400, 458, 840, 960
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 400, 458, 840, 960 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 400, 458, 840, 960. So, keep reading to learn more.
Given numbers are 400,458,840,960
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 400,458,840,960 is 7694400.
Find LCM of 400,458,840,960 with Prime Factorization
| 2 | 400, 458, 840, 960 |
| 2 | 200, 229, 420, 480 |
| 2 | 100, 229, 210, 240 |
| 2 | 50, 229, 105, 120 |
| 3 | 25, 229, 105, 60 |
| 5 | 25, 229, 35, 20 |
| 5, 229, 7, 4 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 5 x 5 x 229 x 7 x 4 = 7694400
Therefore, the lowest common multiple of 400,458,840,960 is 7694400.
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.
400 x 458 x 840 x 960 = 147732480000
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.
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
458 : 1, 2, 229, 458
840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
960 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 400,458,840,960, is 2.
Now, the common factors can be found like this.
400:2x 2x 2x 2x 5x 5
458:2x 229
840:2x 2x 2x 3x 5x 7
960:2x 2x 2x 2x 2x 2x 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 2x 2x 2x 2x 3x 5x 5 = 9600
Therefore, the value for common factors is 9600.
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 = 147732480000/(2x9600)
LCM = 147732480000/19200
LCM = 7694400
Thus, we can understand that the LCM of 400,458,840,960 is 7694400.
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FAQs on LCM of 400, 458, 840, 960
1. What is the LCM of 400, 458, 840, 960?
Answer: LCM of 400, 458, 840, 960 is 7694400.
2. How to calculate the LCM of 400, 458, 840, 960?
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 400, 458, 840, 960.
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}.