LCM of 123, 408, 400, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 123, 408, 400, 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 123, 408, 400, 420. So, keep reading to learn more.
Given numbers are 123,408,400,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 123,408,400,420 is 5854800.
Find LCM of 123,408,400,420 with Prime Factorization
| 2 | 123, 408, 400, 420 |
| 2 | 123, 204, 200, 210 |
| 2 | 123, 102, 100, 105 |
| 3 | 123, 51, 50, 105 |
| 5 | 41, 17, 50, 35 |
| 41, 17, 10, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 41 x 17 x 10 x 7 = 5854800
Therefore, the lowest common multiple of 123,408,400,420 is 5854800.
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 408 x 400 x 420 = 8430912000
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
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
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
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 123,408,400,420, is 1.
Now, the common factors can be found like this.
123:3x 41
408:2x 2x 2x 3x 17
400:2x 2x 2x 2x 5x 5
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.
2x 2x 2x 2x 2x 3x 3x 5 = 1440
Therefore, the value for common factors is 1440.
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 = 8430912000/(1x1440)
LCM = 8430912000/1440
LCM = 5854800
Thus, we can understand that the LCM of 123,408,400,420 is 5854800.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 123, 408, 400, 420
1. What is the LCM of 123, 408, 400, 420?
Answer: LCM of 123, 408, 400, 420 is 5854800.
2. How to calculate the LCM of 123, 408, 400, 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 123, 408, 400, 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}.