LCM of 217, 312, 512, 528, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 217, 312, 512, 528, 420 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, 312, 512, 528, 420. So, keep reading to learn more.
Given numbers are 217,312,512,528,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 217,312,512,528,420 is 238318080.
Find LCM of 217,312,512,528,420 with Prime Factorization
| 2 | 217, 312, 512, 528, 420 |
| 2 | 217, 156, 256, 264, 210 |
| 2 | 217, 78, 128, 132, 105 |
| 2 | 217, 39, 64, 66, 105 |
| 3 | 217, 39, 32, 33, 105 |
| 7 | 217, 13, 32, 11, 35 |
| 31, 13, 32, 11, 5 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 7 x 31 x 13 x 32 x 11 x 5 = 238318080
Therefore, the lowest common multiple of 217,312,512,528,420 is 238318080.
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 312 x 512 x 528 x 420 = 7687187988480
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
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
512 : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
528 : 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 217,312,512,528,420, is 1.
Now, the common factors can be found like this.
217:7x 31
312:2x 2x 2x 3x 13
512:2x 2x 2x 2x 2x 2x 2x 2x 2
528:2x 2x 2x 2x 3x 11
420:2x 2x 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 2x 2x 2x 2x 2x 2x 2x 2x 3x 3x 7 = 32256
Therefore, the value for common factors is 32256.
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 = 7687187988480/(1x32256)
LCM = 7687187988480/32256
LCM = 238318080
Thus, we can understand that the LCM of 217,312,512,528,420 is 238318080.
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FAQs on LCM of 217, 312, 512, 528, 420
1. What is the LCM of 217, 312, 512, 528, 420?
Answer: LCM of 217, 312, 512, 528, 420 is 238318080.
2. How to calculate the LCM of 217, 312, 512, 528, 420?
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, 312, 512, 528, 420.
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}.