LCM of 585, 840, 654, 690
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 585, 840, 654, 690 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 585, 840, 654, 690. So, keep reading to learn more.
Given numbers are 585,840,654,690
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 585,840,654,690 is 82129320.
Find LCM of 585,840,654,690 with Prime Factorization
| 2 | 585, 840, 654, 690 |
| 3 | 585, 420, 327, 345 |
| 5 | 195, 140, 109, 115 |
| 39, 28, 109, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 39 x 28 x 109 x 23 = 82129320
Therefore, the lowest common multiple of 585,840,654,690 is 82129320.
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.
585 x 840 x 654 x 690 = 221749164000
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.
585 : 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585
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
654 : 1, 2, 3, 6, 109, 218, 327, 654
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 585,840,654,690, is 3.
Now, the common factors can be found like this.
585:3x 3x 5x 13
840:2x 2x 2x 3x 5x 7
654:2x 3x 109
690:2x 3x 5x 23
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 3x 3x 5x 5 = 900
Therefore, the value for common factors is 900.
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 = 221749164000/(3x900)
LCM = 221749164000/2700
LCM = 82129320
Thus, we can understand that the LCM of 585,840,654,690 is 82129320.
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FAQs on LCM of 585, 840, 654, 690
1. What is the LCM of 585, 840, 654, 690?
Answer: LCM of 585, 840, 654, 690 is 82129320.
2. How to calculate the LCM of 585, 840, 654, 690?
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 585, 840, 654, 690.
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}.