LCM of 516, 704, 312, 762
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 516, 704, 312, 762 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 516, 704, 312, 762. So, keep reading to learn more.
Given numbers are 516,704,312,762
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 516,704,312,762 is 149937216.
Find LCM of 516,704,312,762 with Prime Factorization
| 2 | 516, 704, 312, 762 |
| 2 | 258, 352, 156, 381 |
| 2 | 129, 176, 78, 381 |
| 3 | 129, 88, 39, 381 |
| 43, 88, 13, 127 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 43 x 88 x 13 x 127 = 149937216
Therefore, the lowest common multiple of 516,704,312,762 is 149937216.
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.
516 x 704 x 312 x 762 = 86363836416
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.
516 : 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516
704 : 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
762 : 1, 2, 3, 6, 127, 254, 381, 762
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 516,704,312,762, is 2.
Now, the common factors can be found like this.
516:2x 2x 3x 43
704:2x 2x 2x 2x 2x 2x 11
312:2x 2x 2x 3x 13
762:2x 3x 127
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 3 = 288
Therefore, the value for common factors is 288.
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 = 86363836416/(2x288)
LCM = 86363836416/576
LCM = 149937216
Thus, we can understand that the LCM of 516,704,312,762 is 149937216.
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FAQs on LCM of 516, 704, 312, 762
1. What is the LCM of 516, 704, 312, 762?
Answer: LCM of 516, 704, 312, 762 is 149937216.
2. How to calculate the LCM of 516, 704, 312, 762?
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 516, 704, 312, 762.
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}.