LCM of 302, 840, 105, 419
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 302, 840, 105, 419 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 302, 840, 105, 419. So, keep reading to learn more.
Given numbers are 302,840,105,419
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 302,840,105,419 is 53145960.
Find LCM of 302,840,105,419 with Prime Factorization
| 2 | 302, 840, 105, 419 |
| 3 | 151, 420, 105, 419 |
| 5 | 151, 140, 35, 419 |
| 7 | 151, 28, 7, 419 |
| 151, 4, 1, 419 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 151 x 4 x 1 x 419 = 53145960
Therefore, the lowest common multiple of 302,840,105,419 is 53145960.
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.
302 x 840 x 105 x 419 = 11160651600
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.
302 : 1, 2, 151, 302
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
105 : 1, 3, 5, 7, 15, 21, 35, 105
419 : 1, 419
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 302,840,105,419, is 1.
Now, the common factors can be found like this.
302:2x 151
840:2x 2x 2x 3x 5x 7
105:3x 5x 7
419:419
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 3x 5x 7 = 210
Therefore, the value for common factors is 210.
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 = 11160651600/(1x210)
LCM = 11160651600/210
LCM = 53145960
Thus, we can understand that the LCM of 302,840,105,419 is 53145960.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 302, 840, 105, 419
1. What is the LCM of 302, 840, 105, 419?
Answer: LCM of 302, 840, 105, 419 is 53145960.
2. How to calculate the LCM of 302, 840, 105, 419?
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 302, 840, 105, 419.
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}.