LCM of 378, 408, 380, 585, 969
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 378, 408, 380, 585, 969 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 378, 408, 380, 585, 969. So, keep reading to learn more.
Given numbers are 378,408,380,585,969
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 378,408,380,585,969 is 31744440.
Find LCM of 378,408,380,585,969 with Prime Factorization
| 2 | 378, 408, 380, 585, 969 |
| 2 | 189, 204, 190, 585, 969 |
| 3 | 189, 102, 95, 585, 969 |
| 3 | 63, 34, 95, 195, 323 |
| 5 | 21, 34, 95, 65, 323 |
| 17 | 21, 34, 19, 13, 323 |
| 19 | 21, 2, 19, 13, 19 |
| 21, 2, 1, 13, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 17 x 19 x 21 x 2 x 1 x 13 x 1 = 31744440
Therefore, the lowest common multiple of 378,408,380,585,969 is 31744440.
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.
378 x 408 x 380 x 585 x 969 = 33221191348800
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.
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
380 : 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
585 : 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585
969 : 1, 3, 17, 19, 51, 57, 323, 969
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 378,408,380,585,969, is 1.
Now, the common factors can be found like this.
378:2x 3x 3x 3x 7
408:2x 2x 2x 3x 17
380:2x 2x 5x 19
585:3x 3x 5x 13
969:3x 17x 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 2x 3x 3x 3x 3x 5x 17x 19 = 1046520
Therefore, the value for common factors is 1046520.
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 = 33221191348800/(1x1046520)
LCM = 33221191348800/1046520
LCM = 31744440
Thus, we can understand that the LCM of 378,408,380,585,969 is 31744440.
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FAQs on LCM of 378, 408, 380, 585, 969
1. What is the LCM of 378, 408, 380, 585, 969?
Answer: LCM of 378, 408, 380, 585, 969 is 31744440.
2. How to calculate the LCM of 378, 408, 380, 585, 969?
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 378, 408, 380, 585, 969.
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}.