LCM of 369, 309, 300, 648, 324
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 369, 309, 300, 648, 324 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 369, 309, 300, 648, 324. So, keep reading to learn more.
Given numbers are 369,309,300,648,324
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 369,309,300,648,324 is 68412600.
Find LCM of 369,309,300,648,324 with Prime Factorization
| 2 | 369, 309, 300, 648, 324 |
| 2 | 369, 309, 150, 324, 162 |
| 3 | 369, 309, 75, 81, 162 |
| 3 | 123, 103, 25, 27, 54 |
| 3 | 41, 103, 25, 9, 18 |
| 3 | 41, 103, 25, 3, 6 |
| 41, 103, 25, 1, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 3 x 3 x 41 x 103 x 25 x 1 x 2 = 68412600
Therefore, the lowest common multiple of 369,309,300,648,324 is 68412600.
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.
369 x 309 x 300 x 648 x 324 = 7181681097600
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.
369 : 1, 3, 9, 41, 123, 369
309 : 1, 3, 103, 309
300 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
648 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
324 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 369,309,300,648,324, is 3.
Now, the common factors can be found like this.
369:3x 3x 41
309:3x 103
300:2x 2x 3x 5x 5
648:2x 2x 2x 3x 3x 3x 3
324:2x 2x 3x 3x 3x 3
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 3x 3x 3x 3x 3x 3x 3 = 34992
Therefore, the value for common factors is 34992.
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 = 7181681097600/(3x34992)
LCM = 7181681097600/104976
LCM = 68412600
Thus, we can understand that the LCM of 369,309,300,648,324 is 68412600.
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FAQs on LCM of 369, 309, 300, 648, 324
1. What is the LCM of 369, 309, 300, 648, 324?
Answer: LCM of 369, 309, 300, 648, 324 is 68412600.
2. How to calculate the LCM of 369, 309, 300, 648, 324?
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 369, 309, 300, 648, 324.
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}.