LCM of 228, 210, 214, 456
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 228, 210, 214, 456 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 228, 210, 214, 456. So, keep reading to learn more.
Given numbers are 228,210,214,456
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 228,210,214,456 is 1707720.
Find LCM of 228,210,214,456 with Prime Factorization
| 2 | 228, 210, 214, 456 |
| 2 | 114, 105, 107, 228 |
| 3 | 57, 105, 107, 114 |
| 19 | 19, 35, 107, 38 |
| 1, 35, 107, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 19 x 1 x 35 x 107 x 2 = 1707720
Therefore, the lowest common multiple of 228,210,214,456 is 1707720.
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.
228 x 210 x 214 x 456 = 4672321920
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.
228 : 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
210 : 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
214 : 1, 2, 107, 214
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 228,210,214,456, is 2.
Now, the common factors can be found like this.
228:2x 2x 3x 19
210:2x 3x 5x 7
214:2x 107
456:2x 2x 2x 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.
2x 2x 2x 3x 3x 19 = 1368
Therefore, the value for common factors is 1368.
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 = 4672321920/(2x1368)
LCM = 4672321920/2736
LCM = 1707720
Thus, we can understand that the LCM of 228,210,214,456 is 1707720.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 228, 210, 214, 456
1. What is the LCM of 228, 210, 214, 456?
Answer: LCM of 228, 210, 214, 456 is 1707720.
2. How to calculate the LCM of 228, 210, 214, 456?
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 228, 210, 214, 456.
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}.