LCM of 420, 493, 348, 710
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 493, 348, 710 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, 493, 348, 710. So, keep reading to learn more.
Given numbers are 420,493,348,710
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,493,348,710 is 14701260.
Find LCM of 420,493,348,710 with Prime Factorization
| 2 | 420, 493, 348, 710 |
| 2 | 210, 493, 174, 355 |
| 3 | 105, 493, 87, 355 |
| 5 | 35, 493, 29, 355 |
| 29 | 7, 493, 29, 71 |
| 7, 17, 1, 71 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 29 x 7 x 17 x 1 x 71 = 14701260
Therefore, the lowest common multiple of 420,493,348,710 is 14701260.
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 493 x 348 x 710 = 51160384800
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
493 : 1, 17, 29, 493
348 : 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348
710 : 1, 2, 5, 10, 71, 142, 355, 710
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,493,348,710, is 1.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
493:17x 29
348:2x 2x 3x 29
710:2x 5x 71
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 29 = 3480
Therefore, the value for common factors is 3480.
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 = 51160384800/(1x3480)
LCM = 51160384800/3480
LCM = 14701260
Thus, we can understand that the LCM of 420,493,348,710 is 14701260.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 420, 493, 348, 710
1. What is the LCM of 420, 493, 348, 710?
Answer: LCM of 420, 493, 348, 710 is 14701260.
2. How to calculate the LCM of 420, 493, 348, 710?
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, 493, 348, 710.
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}.