LCM of 217, 576, 507, 322, 460
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 217, 576, 507, 322, 460 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 217, 576, 507, 322, 460. So, keep reading to learn more.
Given numbers are 217,576,507,322,460
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 217,576,507,322,460 is 2429219520.
Find LCM of 217,576,507,322,460 with Prime Factorization
| 2 | 217, 576, 507, 322, 460 |
| 2 | 217, 288, 507, 161, 230 |
| 3 | 217, 144, 507, 161, 115 |
| 7 | 217, 48, 169, 161, 115 |
| 23 | 31, 48, 169, 23, 115 |
| 31, 48, 169, 1, 5 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 7 x 23 x 31 x 48 x 169 x 1 x 5 = 2429219520
Therefore, the lowest common multiple of 217,576,507,322,460 is 2429219520.
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.
217 x 576 x 507 x 322 x 460 = 9386504225280
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.
217 : 1, 7, 31, 217
576 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
507 : 1, 3, 13, 39, 169, 507
322 : 1, 2, 7, 14, 23, 46, 161, 322
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 217,576,507,322,460, is 1.
Now, the common factors can be found like this.
217:7x 31
576:2x 2x 2x 2x 2x 2x 3x 3
507:3x 13x 13
322:2x 7x 23
460:2x 2x 5x 23
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 3x 7x 23 = 3864
Therefore, the value for common factors is 3864.
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 = 9386504225280/(1x3864)
LCM = 9386504225280/3864
LCM = 2429219520
Thus, we can understand that the LCM of 217,576,507,322,460 is 2429219520.
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FAQs on LCM of 217, 576, 507, 322, 460
1. What is the LCM of 217, 576, 507, 322, 460?
Answer: LCM of 217, 576, 507, 322, 460 is 2429219520.
2. How to calculate the LCM of 217, 576, 507, 322, 460?
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 217, 576, 507, 322, 460.
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}.