LCM of 8, 360, 390, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 8, 360, 390, 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 8, 360, 390, 420. So, keep reading to learn more.
Given numbers are 8,360,390,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 8,360,390,420 is 32760.
Find LCM of 8,360,390,420 with Prime Factorization
| 2 | 8, 360, 390, 420 |
| 2 | 4, 180, 195, 210 |
| 2 | 2, 90, 195, 105 |
| 3 | 1, 45, 195, 105 |
| 5 | 1, 15, 65, 35 |
| 1, 3, 13, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 1 x 3 x 13 x 7 = 32760
Therefore, the lowest common multiple of 8,360,390,420 is 32760.
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.
8 x 360 x 390 x 420 = 471744000
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.
8 : 1, 2, 4, 8
360 : 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
390 : 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
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
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 8,360,390,420, is 2.
Now, the common factors can be found like this.
8:2x 2x 2
360:2x 2x 2x 3x 3x 5
390:2x 3x 5x 13
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 3x 3x 5x 5 = 7200
Therefore, the value for common factors is 7200.
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 = 471744000/(2x7200)
LCM = 471744000/14400
LCM = 32760
Thus, we can understand that the LCM of 8,360,390,420 is 32760.
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FAQs on LCM of 8, 360, 390, 420
1. What is the LCM of 8, 360, 390, 420?
Answer: LCM of 8, 360, 390, 420 is 32760.
2. How to calculate the LCM of 8, 360, 390, 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 8, 360, 390, 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}.