LCM of 317, 690, 756, 240, 105
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 317, 690, 756, 240, 105 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 317, 690, 756, 240, 105. So, keep reading to learn more.
Given numbers are 317,690,756,240,105
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 317,690,756,240,105 is 110239920.
Find LCM of 317,690,756,240,105 with Prime Factorization
| 2 | 317, 690, 756, 240, 105 |
| 2 | 317, 345, 378, 120, 105 |
| 3 | 317, 345, 189, 60, 105 |
| 5 | 317, 115, 63, 20, 35 |
| 7 | 317, 23, 63, 4, 7 |
| 317, 23, 9, 4, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 317 x 23 x 9 x 4 x 1 = 110239920
Therefore, the lowest common multiple of 317,690,756,240,105 is 110239920.
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.
317 x 690 x 756 x 240 x 105 = 4167068976000
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.
317 : 1, 317
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
756 : 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
105 : 1, 3, 5, 7, 15, 21, 35, 105
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 317,690,756,240,105, is 1.
Now, the common factors can be found like this.
317:317
690:2x 3x 5x 23
756:2x 2x 3x 3x 3x 7
240:2x 2x 2x 2x 3x 5
105:3x 5x 7
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 5x 5x 7 = 37800
Therefore, the value for common factors is 37800.
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 = 4167068976000/(1x37800)
LCM = 4167068976000/37800
LCM = 110239920
Thus, we can understand that the LCM of 317,690,756,240,105 is 110239920.
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FAQs on LCM of 317, 690, 756, 240, 105
1. What is the LCM of 317, 690, 756, 240, 105?
Answer: LCM of 317, 690, 756, 240, 105 is 110239920.
2. How to calculate the LCM of 317, 690, 756, 240, 105?
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 317, 690, 756, 240, 105.
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}.