LCM of 509, 146, 120, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 509, 146, 120, 420 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 509, 146, 120, 420. So, keep reading to learn more.
Given numbers are 509,146,120,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 509,146,120,420 is 31211880.
Find LCM of 509,146,120,420 with Prime Factorization
| 2 | 509, 146, 120, 420 |
| 2 | 509, 73, 60, 210 |
| 3 | 509, 73, 30, 105 |
| 5 | 509, 73, 10, 35 |
| 509, 73, 2, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 509 x 73 x 2 x 7 = 31211880
Therefore, the lowest common multiple of 509,146,120,420 is 31211880.
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.
509 x 146 x 120 x 420 = 3745425600
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.
509 : 1, 509
146 : 1, 2, 73, 146
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
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
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 509,146,120,420, is 1.
Now, the common factors can be found like this.
509:509
146:2x 73
120:2x 2x 2x 3x 5
420:2x 2x 3x 5x 7
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 3x 5 = 120
Therefore, the value for common factors is 120.
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 = 3745425600/(1x120)
LCM = 3745425600/120
LCM = 31211880
Thus, we can understand that the LCM of 509,146,120,420 is 31211880.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 509, 146, 120, 420
1. What is the LCM of 509, 146, 120, 420?
Answer: LCM of 509, 146, 120, 420 is 31211880.
2. How to calculate the LCM of 509, 146, 120, 420?
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 509, 146, 120, 420.
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}.