LCM of 585, 414, 429
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 585, 414, 429 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, 414, 429. So, keep reading to learn more.
Given numbers are 585,414,429
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 585,414,429 is 296010.
Find LCM of 585,414,429 with Prime Factorization
| 3 | 585, 414, 429 |
| 3 | 195, 138, 143 |
| 13 | 65, 46, 143 |
| 5, 46, 11 |
Multiply the prime numbers at the bottom and the left side.
3 x 3 x 13 x 5 x 46 x 11 = 296010
Therefore, the lowest common multiple of 585,414,429 is 296010.
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 414 x 429 = 103899510
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
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
429 : 1, 3, 11, 13, 33, 39, 143, 429
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 585,414,429, is 3.
Now, the common factors can be found like this.
585:3x 3x 5x 13
414:2x 3x 3x 23
429:3x 11x 13
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
3x 3x 13 = 117
Therefore, the value for common factors is 117.
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 = 103899510/(3x117)
LCM = 103899510/351
LCM = 296010
Thus, we can understand that the LCM of 585,414,429 is 296010.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 585, 414, 429
1. What is the LCM of 585, 414, 429?
Answer: LCM of 585, 414, 429 is 296010.
2. How to calculate the LCM of 585, 414, 429?
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, 414, 429.
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}.