LCM of 406, 705, 420, 340
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 406, 705, 420, 340 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 406, 705, 420, 340. So, keep reading to learn more.
Given numbers are 406,705,420,340
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 406,705,420,340 is 9731820.
Find LCM of 406,705,420,340 with Prime Factorization
| 2 | 406, 705, 420, 340 |
| 2 | 203, 705, 210, 170 |
| 3 | 203, 705, 105, 85 |
| 5 | 203, 235, 35, 85 |
| 7 | 203, 47, 7, 17 |
| 29, 47, 1, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 29 x 47 x 1 x 17 = 9731820
Therefore, the lowest common multiple of 406,705,420,340 is 9731820.
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.
406 x 705 x 420 x 340 = 40873644000
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.
406 : 1, 2, 7, 14, 29, 58, 203, 406
705 : 1, 3, 5, 15, 47, 141, 235, 705
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
340 : 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 406,705,420,340, is 1.
Now, the common factors can be found like this.
406:2x 7x 29
705:3x 5x 47
420:2x 2x 3x 5x 7
340:2x 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 5x 5x 7 = 4200
Therefore, the value for common factors is 4200.
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 = 40873644000/(1x4200)
LCM = 40873644000/4200
LCM = 9731820
Thus, we can understand that the LCM of 406,705,420,340 is 9731820.
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FAQs on LCM of 406, 705, 420, 340
1. What is the LCM of 406, 705, 420, 340?
Answer: LCM of 406, 705, 420, 340 is 9731820.
2. How to calculate the LCM of 406, 705, 420, 340?
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 406, 705, 420, 340.
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}.