LCM of 429, 420, 285, 513
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 429, 420, 285, 513 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 429, 420, 285, 513. So, keep reading to learn more.
Given numbers are 429,420,285,513
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 429,420,285,513 is 10270260.
Find LCM of 429,420,285,513 with Prime Factorization
| 3 | 429, 420, 285, 513 |
| 5 | 143, 140, 95, 171 |
| 19 | 143, 28, 19, 171 |
| 143, 28, 1, 9 |
Multiply the prime numbers at the bottom and the left side.
3 x 5 x 19 x 143 x 28 x 1 x 9 = 10270260
Therefore, the lowest common multiple of 429,420,285,513 is 10270260.
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.
429 x 420 x 285 x 513 = 26343216900
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.
429 : 1, 3, 11, 13, 33, 39, 143, 429
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
285 : 1, 3, 5, 15, 19, 57, 95, 285
513 : 1, 3, 9, 19, 27, 57, 171, 513
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 429,420,285,513, is 3.
Now, the common factors can be found like this.
429:3x 11x 13
420:2x 2x 3x 5x 7
285:3x 5x 19
513:3x 3x 3x 19
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 5x 19 = 855
Therefore, the value for common factors is 855.
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 = 26343216900/(3x855)
LCM = 26343216900/2565
LCM = 10270260
Thus, we can understand that the LCM of 429,420,285,513 is 10270260.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 429, 420, 285, 513
1. What is the LCM of 429, 420, 285, 513?
Answer: LCM of 429, 420, 285, 513 is 10270260.
2. How to calculate the LCM of 429, 420, 285, 513?
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 429, 420, 285, 513.
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}.