LCM of 144, 345, 426, 460, 705
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 144, 345, 426, 460, 705 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 144, 345, 426, 460, 705. So, keep reading to learn more.
Given numbers are 144,345,426,460,705
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 144,345,426,460,705 is 55260720.
Find LCM of 144,345,426,460,705 with Prime Factorization
| 2 | 144, 345, 426, 460, 705 |
| 2 | 72, 345, 213, 230, 705 |
| 3 | 36, 345, 213, 115, 705 |
| 5 | 12, 115, 71, 115, 235 |
| 23 | 12, 23, 71, 23, 47 |
| 12, 1, 71, 1, 47 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 23 x 12 x 1 x 71 x 1 x 47 = 55260720
Therefore, the lowest common multiple of 144,345,426,460,705 is 55260720.
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.
144 x 345 x 426 x 460 x 705 = 6863381424000
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.
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
345 : 1, 3, 5, 15, 23, 69, 115, 345
426 : 1, 2, 3, 6, 71, 142, 213, 426
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
705 : 1, 3, 5, 15, 47, 141, 235, 705
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 144,345,426,460,705, is 1.
Now, the common factors can be found like this.
144:2x 2x 2x 2x 3x 3
345:3x 5x 23
426:2x 3x 71
460:2x 2x 5x 23
705:3x 5x 47
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 3x 5x 5x 23 = 124200
Therefore, the value for common factors is 124200.
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 = 6863381424000/(1x124200)
LCM = 6863381424000/124200
LCM = 55260720
Thus, we can understand that the LCM of 144,345,426,460,705 is 55260720.
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FAQs on LCM of 144, 345, 426, 460, 705
1. What is the LCM of 144, 345, 426, 460, 705?
Answer: LCM of 144, 345, 426, 460, 705 is 55260720.
2. How to calculate the LCM of 144, 345, 426, 460, 705?
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 144, 345, 426, 460, 705.
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}.