LCM of 214, 960, 972
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 214, 960, 972 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 214, 960, 972. So, keep reading to learn more.
Given numbers are 214,960,972
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 214,960,972 is 8320320.
Find LCM of 214,960,972 with Prime Factorization
| 2 | 214, 960, 972 |
| 2 | 107, 480, 486 |
| 3 | 107, 240, 243 |
| 107, 80, 81 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 107 x 80 x 81 = 8320320
Therefore, the lowest common multiple of 214,960,972 is 8320320.
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.
214 x 960 x 972 = 199687680
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.
214 : 1, 2, 107, 214
960 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
972 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 214,960,972, is 2.
Now, the common factors can be found like this.
214:2x 107
960:2x 2x 2x 2x 2x 2x 3x 5
972:2x 2x 3x 3x 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 3 = 12
Therefore, the value for common factors is 12.
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 = 199687680/(2x12)
LCM = 199687680/24
LCM = 8320320
Thus, we can understand that the LCM of 214,960,972 is 8320320.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 214, 960, 972
1. What is the LCM of 214, 960, 972?
Answer: LCM of 214, 960, 972 is 8320320.
2. How to calculate the LCM of 214, 960, 972?
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 214, 960, 972.
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}.