LCM of 340, 510, 765, 315
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 340, 510, 765, 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 340, 510, 765, 315. So, keep reading to learn more.
Given numbers are 340,510,765,315
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 340,510,765,315 is 21420.
Find LCM of 340,510,765,315 with Prime Factorization
| 2 | 340, 510, 765, 315 |
| 3 | 170, 255, 765, 315 |
| 3 | 170, 85, 255, 105 |
| 5 | 170, 85, 85, 35 |
| 17 | 34, 17, 17, 7 |
| 2, 1, 1, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 5 x 17 x 2 x 1 x 1 x 7 = 21420
Therefore, the lowest common multiple of 340,510,765,315 is 21420.
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.
340 x 510 x 765 x 315 = 41785065000
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.
340 : 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
510 : 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
765 : 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
315 : 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
5 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 340,510,765,315, is 5.
Now, the common factors can be found like this.
340:2x 2x 5x 17
510:2x 3x 5x 17
765:3x 3x 5x 17
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.
2x 3x 3x 3x 5x 5x 17x 17 = 390150
Therefore, the value for common factors is 390150.
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 = 41785065000/(5x390150)
LCM = 41785065000/1950750
LCM = 21420
Thus, we can understand that the LCM of 340,510,765,315 is 21420.
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FAQs on LCM of 340, 510, 765, 315
1. What is the LCM of 340, 510, 765, 315?
Answer: LCM of 340, 510, 765, 315 is 21420.
2. How to calculate the LCM of 340, 510, 765, 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 340, 510, 765, 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}.