LCM of 305, 411, 420, 130
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 305, 411, 420, 130 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 305, 411, 420, 130. So, keep reading to learn more.
Given numbers are 305,411,420,130
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 305,411,420,130 is 45629220.
Find LCM of 305,411,420,130 with Prime Factorization
| 2 | 305, 411, 420, 130 |
| 3 | 305, 411, 210, 65 |
| 5 | 305, 137, 70, 65 |
| 61, 137, 14, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 61 x 137 x 14 x 13 = 45629220
Therefore, the lowest common multiple of 305,411,420,130 is 45629220.
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.
305 x 411 x 420 x 130 = 6844383000
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.
305 : 1, 5, 61, 305
411 : 1, 3, 137, 411
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
130 : 1, 2, 5, 10, 13, 26, 65, 130
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 305,411,420,130, is 1.
Now, the common factors can be found like this.
305:5x 61
411:3x 137
420:2x 2x 3x 5x 7
130:2x 5x 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 3x 5x 5 = 150
Therefore, the value for common factors is 150.
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 = 6844383000/(1x150)
LCM = 6844383000/150
LCM = 45629220
Thus, we can understand that the LCM of 305,411,420,130 is 45629220.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 305, 411, 420, 130
1. What is the LCM of 305, 411, 420, 130?
Answer: LCM of 305, 411, 420, 130 is 45629220.
2. How to calculate the LCM of 305, 411, 420, 130?
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 305, 411, 420, 130.
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}.