LCM of 8, 272, 120, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 8, 272, 120, 312 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 8, 272, 120, 312. So, keep reading to learn more.
Given numbers are 8,272,120,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 8,272,120,312 is 53040.
Find LCM of 8,272,120,312 with Prime Factorization
| 2 | 8, 272, 120, 312 |
| 2 | 4, 136, 60, 156 |
| 2 | 2, 68, 30, 78 |
| 3 | 1, 34, 15, 39 |
| 1, 34, 5, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 1 x 34 x 5 x 13 = 53040
Therefore, the lowest common multiple of 8,272,120,312 is 53040.
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.
8 x 272 x 120 x 312 = 81469440
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.
8 : 1, 2, 4, 8
272 : 1, 2, 4, 8, 16, 17, 34, 68, 136, 272
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
8 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 8,272,120,312, is 8.
Now, the common factors can be found like this.
8:2x 2x 2
272:2x 2x 2x 2x 17
120:2x 2x 2x 3x 5
312:2x 2x 2x 3x 13
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 2x 3 = 192
Therefore, the value for common factors is 192.
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 = 81469440/(8x192)
LCM = 81469440/1536
LCM = 53040
Thus, we can understand that the LCM of 8,272,120,312 is 53040.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 8, 272, 120, 312
1. What is the LCM of 8, 272, 120, 312?
Answer: LCM of 8, 272, 120, 312 is 53040.
2. How to calculate the LCM of 8, 272, 120, 312?
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 8, 272, 120, 312.
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}.