LCM of 428, 700, 351, 972, 214
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 428, 700, 351, 972, 214 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, 700, 351, 972, 214. So, keep reading to learn more.
Given numbers are 428,700,351,972,214
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 428,700,351,972,214 is 236609100.
Find LCM of 428,700,351,972,214 with Prime Factorization
| 2 | 428, 700, 351, 972, 214 |
| 2 | 214, 350, 351, 486, 107 |
| 3 | 107, 175, 351, 243, 107 |
| 3 | 107, 175, 117, 81, 107 |
| 3 | 107, 175, 39, 27, 107 |
| 107 | 107, 175, 13, 9, 107 |
| 1, 175, 13, 9, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 3 x 107 x 1 x 175 x 13 x 9 x 1 = 236609100
Therefore, the lowest common multiple of 428,700,351,972,214 is 236609100.
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 700 x 351 x 972 x 214 = 21874038076800
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
700 : 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700
351 : 1, 3, 9, 13, 27, 39, 117, 351
972 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
214 : 1, 2, 107, 214
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 428,700,351,972,214, is 1.
Now, the common factors can be found like this.
428:2x 2x 107
700:2x 2x 5x 5x 7
351:3x 3x 3x 13
972:2x 2x 3x 3x 3x 3x 3
214:2x 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 2x 2x 3x 3x 3x 107 = 92448
Therefore, the value for common factors is 92448.
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 = 21874038076800/(1x92448)
LCM = 21874038076800/92448
LCM = 236609100
Thus, we can understand that the LCM of 428,700,351,972,214 is 236609100.
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FAQs on LCM of 428, 700, 351, 972, 214
1. What is the LCM of 428, 700, 351, 972, 214?
Answer: LCM of 428, 700, 351, 972, 214 is 236609100.
2. How to calculate the LCM of 428, 700, 351, 972, 214?
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, 700, 351, 972, 214.
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}.