LCM of 502, 600, 312, 840
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 502, 600, 312, 840 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 502, 600, 312, 840. So, keep reading to learn more.
Given numbers are 502,600,312,840
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 502,600,312,840 is 13704600.
Find LCM of 502,600,312,840 with Prime Factorization
| 2 | 502, 600, 312, 840 |
| 2 | 251, 300, 156, 420 |
| 2 | 251, 150, 78, 210 |
| 3 | 251, 75, 39, 105 |
| 5 | 251, 25, 13, 35 |
| 251, 5, 13, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 251 x 5 x 13 x 7 = 13704600
Therefore, the lowest common multiple of 502,600,312,840 is 13704600.
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.
502 x 600 x 312 x 840 = 78938496000
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.
502 : 1, 2, 251, 502
600 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 502,600,312,840, is 2.
Now, the common factors can be found like this.
502:2x 251
600:2x 2x 2x 3x 5x 5
312:2x 2x 2x 3x 13
840:2x 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 3x 3x 5 = 2880
Therefore, the value for common factors is 2880.
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 = 78938496000/(2x2880)
LCM = 78938496000/5760
LCM = 13704600
Thus, we can understand that the LCM of 502,600,312,840 is 13704600.
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FAQs on LCM of 502, 600, 312, 840
1. What is the LCM of 502, 600, 312, 840?
Answer: LCM of 502, 600, 312, 840 is 13704600.
2. How to calculate the LCM of 502, 600, 312, 840?
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 502, 600, 312, 840.
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}.