LCM of 428, 407, 189, 216
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 428, 407, 189, 216 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 428, 407, 189, 216. So, keep reading to learn more.
Given numbers are 428,407,189,216
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 428,407,189,216 is 65846088.
Find LCM of 428,407,189,216 with Prime Factorization
| 2 | 428, 407, 189, 216 |
| 2 | 214, 407, 189, 108 |
| 3 | 107, 407, 189, 54 |
| 3 | 107, 407, 63, 18 |
| 3 | 107, 407, 21, 6 |
| 107, 407, 7, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 3 x 107 x 407 x 7 x 2 = 65846088
Therefore, the lowest common multiple of 428,407,189,216 is 65846088.
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.
428 x 407 x 189 x 216 = 7111377504
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.
428 : 1, 2, 4, 107, 214, 428
407 : 1, 11, 37, 407
189 : 1, 3, 7, 9, 21, 27, 63, 189
216 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 428,407,189,216, is 1.
Now, the common factors can be found like this.
428:2x 2x 107
407:11x 37
189:3x 3x 3x 7
216:2x 2x 2x 3x 3x 3
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 3 = 108
Therefore, the value for common factors is 108.
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 = 7111377504/(1x108)
LCM = 7111377504/108
LCM = 65846088
Thus, we can understand that the LCM of 428,407,189,216 is 65846088.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 428, 407, 189, 216
1. What is the LCM of 428, 407, 189, 216?
Answer: LCM of 428, 407, 189, 216 is 65846088.
2. How to calculate the LCM of 428, 407, 189, 216?
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 428, 407, 189, 216.
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}.