LCM of 900, 210, 165, 102, 315
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 900, 210, 165, 102, 315 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 900, 210, 165, 102, 315. So, keep reading to learn more.
Given numbers are 900,210,165,102,315
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 900,210,165,102,315 is 1178100.
Find LCM of 900,210,165,102,315 with Prime Factorization
| 2 | 900, 210, 165, 102, 315 |
| 3 | 450, 105, 165, 51, 315 |
| 3 | 150, 35, 55, 17, 105 |
| 5 | 50, 35, 55, 17, 35 |
| 7 | 10, 7, 11, 17, 7 |
| 10, 1, 11, 17, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 5 x 7 x 10 x 1 x 11 x 17 x 1 = 1178100
Therefore, the lowest common multiple of 900,210,165,102,315 is 1178100.
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.
900 x 210 x 165 x 102 x 315 = 1001974050000
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.
900 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
210 : 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
165 : 1, 3, 5, 11, 15, 33, 55, 165
102 : 1, 2, 3, 6, 17, 34, 51, 102
315 : 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 900,210,165,102,315, is 3.
Now, the common factors can be found like this.
900:2x 2x 3x 3x 5x 5
210:2x 3x 5x 7
165:3x 5x 11
102:2x 3x 17
315:3x 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 3x 3x 3x 3x 5x 5x 5x 7 = 283500
Therefore, the value for common factors is 283500.
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 = 1001974050000/(3x283500)
LCM = 1001974050000/850500
LCM = 1178100
Thus, we can understand that the LCM of 900,210,165,102,315 is 1178100.
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FAQs on LCM of 900, 210, 165, 102, 315
1. What is the LCM of 900, 210, 165, 102, 315?
Answer: LCM of 900, 210, 165, 102, 315 is 1178100.
2. How to calculate the LCM of 900, 210, 165, 102, 315?
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 900, 210, 165, 102, 315.
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}.