LCM of 240, 305, 172, 669, 720
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 240, 305, 172, 669, 720 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, 305, 172, 669, 720. So, keep reading to learn more.
Given numbers are 240,305,172,669,720
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 240,305,172,669,720 is 421148880.
Find LCM of 240,305,172,669,720 with Prime Factorization
| 2 | 240, 305, 172, 669, 720 |
| 2 | 120, 305, 86, 669, 360 |
| 2 | 60, 305, 43, 669, 180 |
| 2 | 30, 305, 43, 669, 90 |
| 3 | 15, 305, 43, 669, 45 |
| 5 | 5, 305, 43, 223, 15 |
| 1, 61, 43, 223, 3 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 5 x 1 x 61 x 43 x 223 x 3 = 421148880
Therefore, the lowest common multiple of 240,305,172,669,720 is 421148880.
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 305 x 172 x 669 x 720 = 6064543872000
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
305 : 1, 5, 61, 305
172 : 1, 2, 4, 43, 86, 172
669 : 1, 3, 223, 669
720 : 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 240,305,172,669,720, is 1.
Now, the common factors can be found like this.
240:2x 2x 2x 2x 3x 5
305:5x 61
172:2x 2x 43
669:3x 223
720:2x 2x 2x 2x 3x 3x 5
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 2x 2x 3x 3x 5x 5 = 14400
Therefore, the value for common factors is 14400.
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 = 6064543872000/(1x14400)
LCM = 6064543872000/14400
LCM = 421148880
Thus, we can understand that the LCM of 240,305,172,669,720 is 421148880.
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FAQs on LCM of 240, 305, 172, 669, 720
1. What is the LCM of 240, 305, 172, 669, 720?
Answer: LCM of 240, 305, 172, 669, 720 is 421148880.
2. How to calculate the LCM of 240, 305, 172, 669, 720?
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, 305, 172, 669, 720.
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}.