LCM of 820, 387, 309, 315
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 820, 387, 309, 315 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 820, 387, 309, 315. So, keep reading to learn more.
Given numbers are 820,387,309,315
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 820,387,309,315 is 228802140.
Find LCM of 820,387,309,315 with Prime Factorization
| 3 | 820, 387, 309, 315 |
| 3 | 820, 129, 103, 105 |
| 5 | 820, 43, 103, 35 |
| 164, 43, 103, 7 |
Multiply the prime numbers at the bottom and the left side.
3 x 3 x 5 x 164 x 43 x 103 x 7 = 228802140
Therefore, the lowest common multiple of 820,387,309,315 is 228802140.
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.
820 x 387 x 309 x 315 = 30888288900
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.
820 : 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820
387 : 1, 3, 9, 43, 129, 387
309 : 1, 3, 103, 309
315 : 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 820,387,309,315, is 1.
Now, the common factors can be found like this.
820:2x 2x 5x 41
387:3x 3x 43
309:3x 103
315:3x 3x 5x 7
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
3x 3x 3x 5 = 135
Therefore, the value for common factors is 135.
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 = 30888288900/(1x135)
LCM = 30888288900/135
LCM = 228802140
Thus, we can understand that the LCM of 820,387,309,315 is 228802140.
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FAQs on LCM of 820, 387, 309, 315
1. What is the LCM of 820, 387, 309, 315?
Answer: LCM of 820, 387, 309, 315 is 228802140.
2. How to calculate the LCM of 820, 387, 309, 315?
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 820, 387, 309, 315.
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}.