LCM of 312, 189, 576, 493
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 312, 189, 576, 493 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 312, 189, 576, 493. So, keep reading to learn more.
Given numbers are 312,189,576,493
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 312,189,576,493 is 77523264.
Find LCM of 312,189,576,493 with Prime Factorization
| 2 | 312, 189, 576, 493 |
| 2 | 156, 189, 288, 493 |
| 2 | 78, 189, 144, 493 |
| 3 | 39, 189, 72, 493 |
| 3 | 13, 63, 24, 493 |
| 13, 21, 8, 493 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 13 x 21 x 8 x 493 = 77523264
Therefore, the lowest common multiple of 312,189,576,493 is 77523264.
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.
312 x 189 x 576 x 493 = 16745025024
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.
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
189 : 1, 3, 7, 9, 21, 27, 63, 189
576 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
493 : 1, 17, 29, 493
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 312,189,576,493, is 1.
Now, the common factors can be found like this.
312:2x 2x 2x 3x 13
189:3x 3x 3x 7
576:2x 2x 2x 2x 2x 2x 3x 3
493:17x 29
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 3 = 216
Therefore, the value for common factors is 216.
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 = 16745025024/(1x216)
LCM = 16745025024/216
LCM = 77523264
Thus, we can understand that the LCM of 312,189,576,493 is 77523264.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 312, 189, 576, 493
1. What is the LCM of 312, 189, 576, 493?
Answer: LCM of 312, 189, 576, 493 is 77523264.
2. How to calculate the LCM of 312, 189, 576, 493?
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 312, 189, 576, 493.
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}.