LCM of 314, 214, 144, 428
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 314, 214, 144, 428 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 314, 214, 144, 428. So, keep reading to learn more.
Given numbers are 314,214,144,428
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 314,214,144,428 is 2419056.
Find LCM of 314,214,144,428 with Prime Factorization
| 2 | 314, 214, 144, 428 |
| 2 | 157, 107, 72, 214 |
| 107 | 157, 107, 36, 107 |
| 157, 1, 36, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 107 x 157 x 1 x 36 x 1 = 2419056
Therefore, the lowest common multiple of 314,214,144,428 is 2419056.
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.
314 x 214 x 144 x 428 = 4141423872
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.
314 : 1, 2, 157, 314
214 : 1, 2, 107, 214
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
428 : 1, 2, 4, 107, 214, 428
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 314,214,144,428, is 2.
Now, the common factors can be found like this.
314:2x 157
214:2x 107
144:2x 2x 2x 2x 3x 3
428:2x 2x 107
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 107 = 856
Therefore, the value for common factors is 856.
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 = 4141423872/(2x856)
LCM = 4141423872/1712
LCM = 2419056
Thus, we can understand that the LCM of 314,214,144,428 is 2419056.
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FAQs on LCM of 314, 214, 144, 428
1. What is the LCM of 314, 214, 144, 428?
Answer: LCM of 314, 214, 144, 428 is 2419056.
2. How to calculate the LCM of 314, 214, 144, 428?
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 314, 214, 144, 428.
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}.