LCM of 381, 435, 705, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 381, 435, 705, 420 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 381, 435, 705, 420. So, keep reading to learn more.
Given numbers are 381,435,705,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 381,435,705,420 is 72702420.
Find LCM of 381,435,705,420 with Prime Factorization
| 3 | 381, 435, 705, 420 |
| 5 | 127, 145, 235, 140 |
| 127, 29, 47, 28 |
Multiply the prime numbers at the bottom and the left side.
3 x 5 x 127 x 29 x 47 x 28 = 72702420
Therefore, the lowest common multiple of 381,435,705,420 is 72702420.
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.
381 x 435 x 705 x 420 = 49074133500
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.
381 : 1, 3, 127, 381
435 : 1, 3, 5, 15, 29, 87, 145, 435
705 : 1, 3, 5, 15, 47, 141, 235, 705
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
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 381,435,705,420, is 3.
Now, the common factors can be found like this.
381:3x 127
435:3x 5x 29
705:3x 5x 47
420:2x 2x 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.
3x 3x 5x 5 = 225
Therefore, the value for common factors is 225.
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 = 49074133500/(3x225)
LCM = 49074133500/675
LCM = 72702420
Thus, we can understand that the LCM of 381,435,705,420 is 72702420.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 381, 435, 705, 420
1. What is the LCM of 381, 435, 705, 420?
Answer: LCM of 381, 435, 705, 420 is 72702420.
2. How to calculate the LCM of 381, 435, 705, 420?
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 381, 435, 705, 420.
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}.