LCM of 870, 384, 142, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 870, 384, 142, 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 870, 384, 142, 312. So, keep reading to learn more.
Given numbers are 870,384,142,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 870,384,142,312 is 51392640.
Find LCM of 870,384,142,312 with Prime Factorization
| 2 | 870, 384, 142, 312 |
| 2 | 435, 192, 71, 156 |
| 2 | 435, 96, 71, 78 |
| 3 | 435, 48, 71, 39 |
| 145, 16, 71, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 145 x 16 x 71 x 13 = 51392640
Therefore, the lowest common multiple of 870,384,142,312 is 51392640.
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.
870 x 384 x 142 x 312 = 14801080320
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.
870 : 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
384 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
142 : 1, 2, 71, 142
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 870,384,142,312, is 2.
Now, the common factors can be found like this.
870:2x 3x 5x 29
384:2x 2x 2x 2x 2x 2x 2x 3
142:2x 71
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 3x 3 = 144
Therefore, the value for common factors is 144.
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 = 14801080320/(2x144)
LCM = 14801080320/288
LCM = 51392640
Thus, we can understand that the LCM of 870,384,142,312 is 51392640.
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FAQs on LCM of 870, 384, 142, 312
1. What is the LCM of 870, 384, 142, 312?
Answer: LCM of 870, 384, 142, 312 is 51392640.
2. How to calculate the LCM of 870, 384, 142, 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 870, 384, 142, 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}.