LCM of 828, 440, 378, 156, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 828, 440, 378, 156, 414 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 828, 440, 378, 156, 414. So, keep reading to learn more.
Given numbers are 828,440,378,156,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 828,440,378,156,414 is 24864840.
Find LCM of 828,440,378,156,414 with Prime Factorization
| 2 | 828, 440, 378, 156, 414 |
| 2 | 414, 220, 189, 78, 207 |
| 3 | 207, 110, 189, 39, 207 |
| 3 | 69, 110, 63, 13, 69 |
| 23 | 23, 110, 21, 13, 23 |
| 1, 110, 21, 13, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 23 x 1 x 110 x 21 x 13 x 1 = 24864840
Therefore, the lowest common multiple of 828,440,378,156,414 is 24864840.
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.
828 x 440 x 378 x 156 x 414 = 8894053808640
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.
828 : 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
440 : 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
156 : 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 828,440,378,156,414, is 2.
Now, the common factors can be found like this.
828:2x 2x 3x 3x 23
440:2x 2x 2x 5x 11
378:2x 3x 3x 3x 7
156:2x 2x 3x 13
414:2x 3x 3x 23
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 2x 2x 3x 3x 3x 3x 3x 23 = 178848
Therefore, the value for common factors is 178848.
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 = 8894053808640/(2x178848)
LCM = 8894053808640/357696
LCM = 24864840
Thus, we can understand that the LCM of 828,440,378,156,414 is 24864840.
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FAQs on LCM of 828, 440, 378, 156, 414
1. What is the LCM of 828, 440, 378, 156, 414?
Answer: LCM of 828, 440, 378, 156, 414 is 24864840.
2. How to calculate the LCM of 828, 440, 378, 156, 414?
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 828, 440, 378, 156, 414.
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}.