LCM of 419, 306, 338, 720, 624
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 419, 306, 338, 720, 624 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 419, 306, 338, 720, 624. So, keep reading to learn more.
Given numbers are 419,306,338,720,624
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 419,306,338,720,624 is 866726640.
Find LCM of 419,306,338,720,624 with Prime Factorization
| 2 | 419, 306, 338, 720, 624 |
| 2 | 419, 153, 169, 360, 312 |
| 2 | 419, 153, 169, 180, 156 |
| 2 | 419, 153, 169, 90, 78 |
| 3 | 419, 153, 169, 45, 39 |
| 3 | 419, 51, 169, 15, 13 |
| 13 | 419, 17, 169, 5, 13 |
| 419, 17, 1, 5, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 3 x 13 x 419 x 17 x 1 x 5 x 13 = 866726640
Therefore, the lowest common multiple of 419,306,338,720,624 is 866726640.
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.
419 x 306 x 338 x 720 x 624 = 19470147240960
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.
419 : 1, 419
306 : 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
338 : 1, 2, 13, 26, 169, 338
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
624 : 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 419,306,338,720,624, is 1.
Now, the common factors can be found like this.
419:419
306:2x 3x 3x 17
338:2x 13x 13
720:2x 2x 2x 2x 3x 3x 5
624:2x 2x 2x 2x 3x 13
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 3x 3x 3x 13 = 22464
Therefore, the value for common factors is 22464.
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 = 19470147240960/(1x22464)
LCM = 19470147240960/22464
LCM = 866726640
Thus, we can understand that the LCM of 419,306,338,720,624 is 866726640.
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FAQs on LCM of 419, 306, 338, 720, 624
1. What is the LCM of 419, 306, 338, 720, 624?
Answer: LCM of 419, 306, 338, 720, 624 is 866726640.
2. How to calculate the LCM of 419, 306, 338, 720, 624?
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 419, 306, 338, 720, 624.
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}.