LCM of 310, 596, 420, 465, 258
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 310, 596, 420, 465, 258 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 310, 596, 420, 465, 258. So, keep reading to learn more.
Given numbers are 310,596,420,465,258
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 310,596,420,465,258 is 83419140.
Find LCM of 310,596,420,465,258 with Prime Factorization
| 2 | 310, 596, 420, 465, 258 |
| 2 | 155, 298, 210, 465, 129 |
| 3 | 155, 149, 105, 465, 129 |
| 5 | 155, 149, 35, 155, 43 |
| 31 | 31, 149, 7, 31, 43 |
| 1, 149, 7, 1, 43 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 31 x 1 x 149 x 7 x 1 x 43 = 83419140
Therefore, the lowest common multiple of 310,596,420,465,258 is 83419140.
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.
310 x 596 x 420 x 465 x 258 = 9309576024000
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.
310 : 1, 2, 5, 10, 31, 62, 155, 310
596 : 1, 2, 4, 149, 298, 596
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
465 : 1, 3, 5, 15, 31, 93, 155, 465
258 : 1, 2, 3, 6, 43, 86, 129, 258
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 310,596,420,465,258, is 1.
Now, the common factors can be found like this.
310:2x 5x 31
596:2x 2x 149
420:2x 2x 3x 5x 7
465:3x 5x 31
258:2x 3x 43
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 3x 3x 5x 5x 31 = 111600
Therefore, the value for common factors is 111600.
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 = 9309576024000/(1x111600)
LCM = 9309576024000/111600
LCM = 83419140
Thus, we can understand that the LCM of 310,596,420,465,258 is 83419140.
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FAQs on LCM of 310, 596, 420, 465, 258
1. What is the LCM of 310, 596, 420, 465, 258?
Answer: LCM of 310, 596, 420, 465, 258 is 83419140.
2. How to calculate the LCM of 310, 596, 420, 465, 258?
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 310, 596, 420, 465, 258.
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}.