LCM of 312, 382, 468, 972
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 312, 382, 468, 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 312, 382, 468, 972. So, keep reading to learn more.
Given numbers are 312,382,468,972
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 312,382,468,972 is 4826952.
Find LCM of 312,382,468,972 with Prime Factorization
| 2 | 312, 382, 468, 972 |
| 2 | 156, 191, 234, 486 |
| 3 | 78, 191, 117, 243 |
| 3 | 26, 191, 39, 81 |
| 13 | 26, 191, 13, 27 |
| 2, 191, 1, 27 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 13 x 2 x 191 x 1 x 27 = 4826952
Therefore, the lowest common multiple of 312,382,468,972 is 4826952.
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.
312 x 382 x 468 x 972 = 54216324864
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.
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
382 : 1, 2, 191, 382
468 : 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468
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 312,382,468,972, is 2.
Now, the common factors can be found like this.
312:2x 2x 2x 3x 13
382:2x 191
468:2x 2x 3x 3x 13
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 2x 2x 3x 3x 3x 13 = 5616
Therefore, the value for common factors is 5616.
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 = 54216324864/(2x5616)
LCM = 54216324864/11232
LCM = 4826952
Thus, we can understand that the LCM of 312,382,468,972 is 4826952.
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FAQs on LCM of 312, 382, 468, 972
1. What is the LCM of 312, 382, 468, 972?
Answer: LCM of 312, 382, 468, 972 is 4826952.
2. How to calculate the LCM of 312, 382, 468, 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 312, 382, 468, 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}.