LCM of 309, 210, 812, 965, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 309, 210, 812, 965, 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 309, 210, 812, 965, 420. So, keep reading to learn more.
Given numbers are 309,210,812,965,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 309,210,812,965,420 is 242126220.
Find LCM of 309,210,812,965,420 with Prime Factorization
| 2 | 309, 210, 812, 965, 420 |
| 2 | 309, 105, 406, 965, 210 |
| 3 | 309, 105, 203, 965, 105 |
| 5 | 103, 35, 203, 965, 35 |
| 7 | 103, 7, 203, 193, 7 |
| 103, 1, 29, 193, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 103 x 1 x 29 x 193 x 1 = 242126220
Therefore, the lowest common multiple of 309,210,812,965,420 is 242126220.
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.
309 x 210 x 812 x 965 x 420 = 21355532604000
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.
309 : 1, 3, 103, 309
210 : 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
812 : 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
965 : 1, 5, 193, 965
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
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 309,210,812,965,420, is 1.
Now, the common factors can be found like this.
309:3x 103
210:2x 3x 5x 7
812:2x 2x 7x 29
965:5x 193
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 3x 3x 5x 5x 7x 7 = 88200
Therefore, the value for common factors is 88200.
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 = 21355532604000/(1x88200)
LCM = 21355532604000/88200
LCM = 242126220
Thus, we can understand that the LCM of 309,210,812,965,420 is 242126220.
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FAQs on LCM of 309, 210, 812, 965, 420
1. What is the LCM of 309, 210, 812, 965, 420?
Answer: LCM of 309, 210, 812, 965, 420 is 242126220.
2. How to calculate the LCM of 309, 210, 812, 965, 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 309, 210, 812, 965, 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}.