LCM of 420, 270, 298, 509
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 270, 298, 509 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, 270, 298, 509. So, keep reading to learn more.
Given numbers are 420,270,298,509
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,270,298,509 is 286678980.
Find LCM of 420,270,298,509 with Prime Factorization
| 2 | 420, 270, 298, 509 |
| 3 | 210, 135, 149, 509 |
| 5 | 70, 45, 149, 509 |
| 14, 9, 149, 509 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 14 x 9 x 149 x 509 = 286678980
Therefore, the lowest common multiple of 420,270,298,509 is 286678980.
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 270 x 298 x 509 = 17200738800
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
270 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
298 : 1, 2, 149, 298
509 : 1, 509
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,270,298,509, is 1.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
270:2x 3x 3x 3x 5
298:2x 149
509:509
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 5 = 60
Therefore, the value for common factors is 60.
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 = 17200738800/(1x60)
LCM = 17200738800/60
LCM = 286678980
Thus, we can understand that the LCM of 420,270,298,509 is 286678980.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 420, 270, 298, 509
1. What is the LCM of 420, 270, 298, 509?
Answer: LCM of 420, 270, 298, 509 is 286678980.
2. How to calculate the LCM of 420, 270, 298, 509?
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, 270, 298, 509.
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}.