LCM of 420, 257, 578, 840
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 257, 578, 840 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 420, 257, 578, 840. So, keep reading to learn more.
Given numbers are 420,257,578,840
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,257,578,840 is 62389320.
Find LCM of 420,257,578,840 with Prime Factorization
| 2 | 420, 257, 578, 840 |
| 2 | 210, 257, 289, 420 |
| 3 | 105, 257, 289, 210 |
| 5 | 35, 257, 289, 70 |
| 7 | 7, 257, 289, 14 |
| 1, 257, 289, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 1 x 257 x 289 x 2 = 62389320
Therefore, the lowest common multiple of 420,257,578,840 is 62389320.
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.
420 x 257 x 578 x 840 = 52407028800
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.
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
257 : 1, 257
578 : 1, 2, 17, 34, 289, 578
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
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,257,578,840, is 1.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
257:257
578:2x 17x 17
840:2x 2x 2x 3x 5x 7
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 5x 7 = 840
Therefore, the value for common factors is 840.
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 = 52407028800/(1x840)
LCM = 52407028800/840
LCM = 62389320
Thus, we can understand that the LCM of 420,257,578,840 is 62389320.
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FAQs on LCM of 420, 257, 578, 840
1. What is the LCM of 420, 257, 578, 840?
Answer: LCM of 420, 257, 578, 840 is 62389320.
2. How to calculate the LCM of 420, 257, 578, 840?
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 420, 257, 578, 840.
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}.