LCM of 240, 209, 510, 312, 363
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 240, 209, 510, 312, 363 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 240, 209, 510, 312, 363. So, keep reading to learn more.
Given numbers are 240,209,510,312,363
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 240,209,510,312,363 is 121938960.
Find LCM of 240,209,510,312,363 with Prime Factorization
| 2 | 240, 209, 510, 312, 363 |
| 2 | 120, 209, 255, 156, 363 |
| 2 | 60, 209, 255, 78, 363 |
| 3 | 30, 209, 255, 39, 363 |
| 5 | 10, 209, 85, 13, 121 |
| 11 | 2, 209, 17, 13, 121 |
| 2, 19, 17, 13, 11 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 11 x 2 x 19 x 17 x 13 x 11 = 121938960
Therefore, the lowest common multiple of 240,209,510,312,363 is 121938960.
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.
240 x 209 x 510 x 312 x 363 = 2897269689600
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.
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
209 : 1, 11, 19, 209
510 : 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
363 : 1, 3, 11, 33, 121, 363
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 240,209,510,312,363, is 1.
Now, the common factors can be found like this.
240:2x 2x 2x 2x 3x 5
209:11x 19
510:2x 3x 5x 17
312:2x 2x 2x 3x 13
363:3x 11x 11
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 5x 11 = 23760
Therefore, the value for common factors is 23760.
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 = 2897269689600/(1x23760)
LCM = 2897269689600/23760
LCM = 121938960
Thus, we can understand that the LCM of 240,209,510,312,363 is 121938960.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 240, 209, 510, 312, 363
1. What is the LCM of 240, 209, 510, 312, 363?
Answer: LCM of 240, 209, 510, 312, 363 is 121938960.
2. How to calculate the LCM of 240, 209, 510, 312, 363?
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 240, 209, 510, 312, 363.
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}.