LCM of 123, 420, 129, 268, 405
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 123, 420, 129, 268, 405 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 123, 420, 129, 268, 405. So, keep reading to learn more.
Given numbers are 123,420,129,268,405
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 123,420,129,268,405 is 1339492140.
Find LCM of 123,420,129,268,405 with Prime Factorization
| 2 | 123, 420, 129, 268, 405 |
| 2 | 123, 210, 129, 134, 405 |
| 3 | 123, 105, 129, 67, 405 |
| 5 | 41, 35, 43, 67, 135 |
| 41, 7, 43, 67, 27 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 41 x 7 x 43 x 67 x 27 = 1339492140
Therefore, the lowest common multiple of 123,420,129,268,405 is 1339492140.
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.
123 x 420 x 129 x 268 x 405 = 723325755600
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.
123 : 1, 3, 41, 123
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
129 : 1, 3, 43, 129
268 : 1, 2, 4, 67, 134, 268
405 : 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 123,420,129,268,405, is 1.
Now, the common factors can be found like this.
123:3x 41
420:2x 2x 3x 5x 7
129:3x 43
268:2x 2x 67
405:3x 3x 3x 3x 5
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 3x 5 = 540
Therefore, the value for common factors is 540.
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 = 723325755600/(1x540)
LCM = 723325755600/540
LCM = 1339492140
Thus, we can understand that the LCM of 123,420,129,268,405 is 1339492140.
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FAQs on LCM of 123, 420, 129, 268, 405
1. What is the LCM of 123, 420, 129, 268, 405?
Answer: LCM of 123, 420, 129, 268, 405 is 1339492140.
2. How to calculate the LCM of 123, 420, 129, 268, 405?
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 123, 420, 129, 268, 405.
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}.