LCM of 280, 378, 409, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 280, 378, 409, 312 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 280, 378, 409, 312. So, keep reading to learn more.
Given numbers are 280,378,409,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 280,378,409,312 is 40196520.
Find LCM of 280,378,409,312 with Prime Factorization
| 2 | 280, 378, 409, 312 |
| 2 | 140, 189, 409, 156 |
| 2 | 70, 189, 409, 78 |
| 3 | 35, 189, 409, 39 |
| 7 | 35, 63, 409, 13 |
| 5, 9, 409, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 7 x 5 x 9 x 409 x 13 = 40196520
Therefore, the lowest common multiple of 280,378,409,312 is 40196520.
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.
280 x 378 x 409 x 312 = 13506030720
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.
280 : 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
409 : 1, 409
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 280,378,409,312, is 1.
Now, the common factors can be found like this.
280:2x 2x 2x 5x 7
378:2x 3x 3x 3x 7
409:409
312:2x 2x 2x 3x 13
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 3x 7 = 336
Therefore, the value for common factors is 336.
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 = 13506030720/(1x336)
LCM = 13506030720/336
LCM = 40196520
Thus, we can understand that the LCM of 280,378,409,312 is 40196520.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 280, 378, 409, 312
1. What is the LCM of 280, 378, 409, 312?
Answer: LCM of 280, 378, 409, 312 is 40196520.
2. How to calculate the LCM of 280, 378, 409, 312?
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 280, 378, 409, 312.
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}.