LCM of 409, 686, 980, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 409, 686, 980, 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 409, 686, 980, 312. So, keep reading to learn more.
Given numbers are 409,686,980,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 409,686,980,312 is 218847720.
Find LCM of 409,686,980,312 with Prime Factorization
| 2 | 409, 686, 980, 312 |
| 2 | 409, 343, 490, 156 |
| 7 | 409, 343, 245, 78 |
| 7 | 409, 49, 35, 78 |
| 409, 7, 5, 78 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 7 x 7 x 409 x 7 x 5 x 78 = 218847720
Therefore, the lowest common multiple of 409,686,980,312 is 218847720.
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.
409 x 686 x 980 x 312 = 85788306240
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.
409 : 1, 409
686 : 1, 2, 7, 14, 49, 98, 343, 686
980 : 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
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 409,686,980,312, is 1.
Now, the common factors can be found like this.
409:409
686:2x 7x 7x 7
980:2x 2x 5x 7x 7
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 7x 7 = 392
Therefore, the value for common factors is 392.
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 = 85788306240/(1x392)
LCM = 85788306240/392
LCM = 218847720
Thus, we can understand that the LCM of 409,686,980,312 is 218847720.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 409, 686, 980, 312
1. What is the LCM of 409, 686, 980, 312?
Answer: LCM of 409, 686, 980, 312 is 218847720.
2. How to calculate the LCM of 409, 686, 980, 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 409, 686, 980, 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}.