LCM of 214, 506, 828, 342
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 214, 506, 828, 342 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 214, 506, 828, 342. So, keep reading to learn more.
Given numbers are 214,506,828,342
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 214,506,828,342 is 18516564.
Find LCM of 214,506,828,342 with Prime Factorization
| 2 | 214, 506, 828, 342 |
| 3 | 107, 253, 414, 171 |
| 3 | 107, 253, 138, 57 |
| 23 | 107, 253, 46, 19 |
| 107, 11, 2, 19 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 23 x 107 x 11 x 2 x 19 = 18516564
Therefore, the lowest common multiple of 214,506,828,342 is 18516564.
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.
214 x 506 x 828 x 342 = 30663429984
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.
214 : 1, 2, 107, 214
506 : 1, 2, 11, 22, 23, 46, 253, 506
828 : 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
342 : 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 214,506,828,342, is 2.
Now, the common factors can be found like this.
214:2x 107
506:2x 11x 23
828:2x 2x 3x 3x 23
342:2x 3x 3x 19
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 3x 3x 23 = 828
Therefore, the value for common factors is 828.
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 = 30663429984/(2x828)
LCM = 30663429984/1656
LCM = 18516564
Thus, we can understand that the LCM of 214,506,828,342 is 18516564.
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FAQs on LCM of 214, 506, 828, 342
1. What is the LCM of 214, 506, 828, 342?
Answer: LCM of 214, 506, 828, 342 is 18516564.
2. How to calculate the LCM of 214, 506, 828, 342?
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 214, 506, 828, 342.
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}.