LCM of 840, 714, 960, 642
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 840, 714, 960, 642 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 840, 714, 960, 642. So, keep reading to learn more.
Given numbers are 840,714,960,642
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 840,714,960,642 is 12223680.
Find LCM of 840,714,960,642 with Prime Factorization
| 2 | 840, 714, 960, 642 |
| 2 | 420, 357, 480, 321 |
| 2 | 210, 357, 240, 321 |
| 3 | 105, 357, 120, 321 |
| 5 | 35, 119, 40, 107 |
| 7 | 7, 119, 8, 107 |
| 1, 17, 8, 107 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 7 x 1 x 17 x 8 x 107 = 12223680
Therefore, the lowest common multiple of 840,714,960,642 is 12223680.
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.
840 x 714 x 960 x 642 = 369644083200
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.
840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
714 : 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
960 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
642 : 1, 2, 3, 6, 107, 214, 321, 642
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 840,714,960,642, is 6.
Now, the common factors can be found like this.
840:2x 2x 2x 3x 5x 7
714:2x 3x 7x 17
960:2x 2x 2x 2x 2x 2x 3x 5
642:2x 3x 107
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 3x 5x 7 = 5040
Therefore, the value for common factors is 5040.
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 = 369644083200/(6x5040)
LCM = 369644083200/30240
LCM = 12223680
Thus, we can understand that the LCM of 840,714,960,642 is 12223680.
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FAQs on LCM of 840, 714, 960, 642
1. What is the LCM of 840, 714, 960, 642?
Answer: LCM of 840, 714, 960, 642 is 12223680.
2. How to calculate the LCM of 840, 714, 960, 642?
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 840, 714, 960, 642.
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}.