LCM of 715, 498, 378, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 715, 498, 378, 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 715, 498, 378, 312. So, keep reading to learn more.
Given numbers are 715,498,378,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 715,498,378,312 is 89729640.
Find LCM of 715,498,378,312 with Prime Factorization
| 2 | 715, 498, 378, 312 |
| 3 | 715, 249, 189, 156 |
| 13 | 715, 83, 63, 52 |
| 55, 83, 63, 4 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 13 x 55 x 83 x 63 x 4 = 89729640
Therefore, the lowest common multiple of 715,498,378,312 is 89729640.
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.
715 x 498 x 378 x 312 = 41993471520
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.
715 : 1, 5, 11, 13, 55, 65, 143, 715
498 : 1, 2, 3, 6, 83, 166, 249, 498
378 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 715,498,378,312, is 1.
Now, the common factors can be found like this.
715:5x 11x 13
498:2x 3x 83
378:2x 3x 3x 3x 7
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 3x 3x 13 = 468
Therefore, the value for common factors is 468.
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 = 41993471520/(1x468)
LCM = 41993471520/468
LCM = 89729640
Thus, we can understand that the LCM of 715,498,378,312 is 89729640.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 715, 498, 378, 312
1. What is the LCM of 715, 498, 378, 312?
Answer: LCM of 715, 498, 378, 312 is 89729640.
2. How to calculate the LCM of 715, 498, 378, 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 715, 498, 378, 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}.