LCM of 405, 720, 420, 319
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 405, 720, 420, 319 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 405, 720, 420, 319. So, keep reading to learn more.
Given numbers are 405,720,420,319
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 405,720,420,319 is 14469840.
Find LCM of 405,720,420,319 with Prime Factorization
| 2 | 405, 720, 420, 319 |
| 2 | 405, 360, 210, 319 |
| 3 | 405, 180, 105, 319 |
| 3 | 135, 60, 35, 319 |
| 5 | 45, 20, 35, 319 |
| 9, 4, 7, 319 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 9 x 4 x 7 x 319 = 14469840
Therefore, the lowest common multiple of 405,720,420,319 is 14469840.
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.
405 x 720 x 420 x 319 = 39068568000
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.
405 : 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
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
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
319 : 1, 11, 29, 319
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 405,720,420,319, is 1.
Now, the common factors can be found like this.
405:3x 3x 3x 3x 5
720:2x 2x 2x 2x 3x 3x 5
420:2x 2x 3x 5x 7
319:11x 29
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 3x 3x 5x 5 = 2700
Therefore, the value for common factors is 2700.
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 = 39068568000/(1x2700)
LCM = 39068568000/2700
LCM = 14469840
Thus, we can understand that the LCM of 405,720,420,319 is 14469840.
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FAQs on LCM of 405, 720, 420, 319
1. What is the LCM of 405, 720, 420, 319?
Answer: LCM of 405, 720, 420, 319 is 14469840.
2. How to calculate the LCM of 405, 720, 420, 319?
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 405, 720, 420, 319.
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}.