LCM of 420, 496, 309, 230, 975
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 496, 309, 230, 975 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 420, 496, 309, 230, 975. So, keep reading to learn more.
Given numbers are 420,496,309,230,975
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,496,309,230,975 is 8019538800.
Find LCM of 420,496,309,230,975 with Prime Factorization
| 2 | 420, 496, 309, 230, 975 |
| 2 | 210, 248, 309, 115, 975 |
| 3 | 105, 124, 309, 115, 975 |
| 5 | 35, 124, 103, 115, 325 |
| 7, 124, 103, 23, 65 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 124 x 103 x 23 x 65 = 8019538800
Therefore, the lowest common multiple of 420,496,309,230,975 is 8019538800.
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.
420 x 496 x 309 x 230 x 975 = 14435169840000
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.
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
496 : 1, 2, 4, 8, 16, 31, 62, 124, 248, 496
309 : 1, 3, 103, 309
230 : 1, 2, 5, 10, 23, 46, 115, 230
975 : 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,496,309,230,975, is 1.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
496:2x 2x 2x 2x 31
309:3x 103
230:2x 5x 23
975:3x 5x 5x 13
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 5 = 1800
Therefore, the value for common factors is 1800.
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 = 14435169840000/(1x1800)
LCM = 14435169840000/1800
LCM = 8019538800
Thus, we can understand that the LCM of 420,496,309,230,975 is 8019538800.
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FAQs on LCM of 420, 496, 309, 230, 975
1. What is the LCM of 420, 496, 309, 230, 975?
Answer: LCM of 420, 496, 309, 230, 975 is 8019538800.
2. How to calculate the LCM of 420, 496, 309, 230, 975?
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 420, 496, 309, 230, 975.
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}.