LCM of 310, 966, 960, 301, 978
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 310, 966, 960, 301, 978 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, 966, 960, 301, 978. So, keep reading to learn more.
Given numbers are 310,966,960,301,978
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 310,966,960,301,978 is 33582642240.
Find LCM of 310,966,960,301,978 with Prime Factorization
| 2 | 310, 966, 960, 301, 978 |
| 3 | 155, 483, 480, 301, 489 |
| 5 | 155, 161, 160, 301, 163 |
| 7 | 31, 161, 32, 301, 163 |
| 31, 23, 32, 43, 163 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 31 x 23 x 32 x 43 x 163 = 33582642240
Therefore, the lowest common multiple of 310,966,960,301,978 is 33582642240.
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 966 x 960 x 301 x 978 = 84628258444800
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
966 : 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966
960 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
301 : 1, 7, 43, 301
978 : 1, 2, 3, 6, 163, 326, 489, 978
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 310,966,960,301,978, is 1.
Now, the common factors can be found like this.
310:2x 5x 31
966:2x 3x 7x 23
960:2x 2x 2x 2x 2x 2x 3x 5
301:7x 43
978:2x 3x 163
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 3x 5x 7 = 2520
Therefore, the value for common factors is 2520.
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 = 84628258444800/(1x2520)
LCM = 84628258444800/2520
LCM = 33582642240
Thus, we can understand that the LCM of 310,966,960,301,978 is 33582642240.
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FAQs on LCM of 310, 966, 960, 301, 978
1. What is the LCM of 310, 966, 960, 301, 978?
Answer: LCM of 310, 966, 960, 301, 978 is 33582642240.
2. How to calculate the LCM of 310, 966, 960, 301, 978?
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, 966, 960, 301, 978.
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}.