LCM of 420, 309, 510, 680
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 309, 510, 680 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, 309, 510, 680. So, keep reading to learn more.
Given numbers are 420,309,510,680
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,309,510,680 is 1470840.
Find LCM of 420,309,510,680 with Prime Factorization
| 2 | 420, 309, 510, 680 |
| 2 | 210, 309, 255, 340 |
| 3 | 105, 309, 255, 170 |
| 5 | 35, 103, 85, 170 |
| 17 | 7, 103, 17, 34 |
| 7, 103, 1, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 17 x 7 x 103 x 1 x 2 = 1470840
Therefore, the lowest common multiple of 420,309,510,680 is 1470840.
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 309 x 510 x 680 = 45007704000
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
309 : 1, 3, 103, 309
510 : 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
680 : 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,309,510,680, is 1.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
309:3x 103
510:2x 3x 5x 17
680:2x 2x 2x 5x 17
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 3x 5x 5x 17 = 30600
Therefore, the value for common factors is 30600.
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 = 45007704000/(1x30600)
LCM = 45007704000/30600
LCM = 1470840
Thus, we can understand that the LCM of 420,309,510,680 is 1470840.
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FAQs on LCM of 420, 309, 510, 680
1. What is the LCM of 420, 309, 510, 680?
Answer: LCM of 420, 309, 510, 680 is 1470840.
2. How to calculate the LCM of 420, 309, 510, 680?
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, 309, 510, 680.
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}.