LCM of 344, 514, 690, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 344, 514, 690, 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 344, 514, 690, 420. So, keep reading to learn more.
Given numbers are 344,514,690,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 344,514,690,420 is 213505320.
Find LCM of 344,514,690,420 with Prime Factorization
| 2 | 344, 514, 690, 420 |
| 2 | 172, 257, 345, 210 |
| 3 | 86, 257, 345, 105 |
| 5 | 86, 257, 115, 35 |
| 86, 257, 23, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 86 x 257 x 23 x 7 = 213505320
Therefore, the lowest common multiple of 344,514,690,420 is 213505320.
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.
344 x 514 x 690 x 420 = 51241276800
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.
344 : 1, 2, 4, 8, 43, 86, 172, 344
514 : 1, 2, 257, 514
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
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
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 344,514,690,420, is 2.
Now, the common factors can be found like this.
344:2x 2x 2x 43
514:2x 257
690:2x 3x 5x 23
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 = 51241276800/(2x120)
LCM = 51241276800/240
LCM = 213505320
Thus, we can understand that the LCM of 344,514,690,420 is 213505320.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 344, 514, 690, 420
1. What is the LCM of 344, 514, 690, 420?
Answer: LCM of 344, 514, 690, 420 is 213505320.
2. How to calculate the LCM of 344, 514, 690, 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 344, 514, 690, 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}.