LCM of 820, 312, 456, 507
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 820, 312, 456, 507 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, 312, 456, 507. So, keep reading to learn more.
Given numbers are 820,312,456,507
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 820,312,456,507 is 15798120.
Find LCM of 820,312,456,507 with Prime Factorization
| 2 | 820, 312, 456, 507 |
| 2 | 410, 156, 228, 507 |
| 2 | 205, 78, 114, 507 |
| 3 | 205, 39, 57, 507 |
| 13 | 205, 13, 19, 169 |
| 205, 1, 19, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 13 x 205 x 1 x 19 x 13 = 15798120
Therefore, the lowest common multiple of 820,312,456,507 is 15798120.
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 312 x 456 x 507 = 59148161280
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
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
507 : 1, 3, 13, 39, 169, 507
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 820,312,456,507, is 1.
Now, the common factors can be found like this.
820:2x 2x 5x 41
312:2x 2x 2x 3x 13
456:2x 2x 2x 3x 19
507:3x 13x 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 2x 3x 3x 13 = 3744
Therefore, the value for common factors is 3744.
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 = 59148161280/(1x3744)
LCM = 59148161280/3744
LCM = 15798120
Thus, we can understand that the LCM of 820,312,456,507 is 15798120.
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FAQs on LCM of 820, 312, 456, 507
1. What is the LCM of 820, 312, 456, 507?
Answer: LCM of 820, 312, 456, 507 is 15798120.
2. How to calculate the LCM of 820, 312, 456, 507?
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, 312, 456, 507.
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}.