LCM of 860, 742, 105, 144, 345
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 860, 742, 105, 144, 345 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 860, 742, 105, 144, 345. So, keep reading to learn more.
Given numbers are 860,742,105,144,345
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 860,742,105,144,345 is 264181680.
Find LCM of 860,742,105,144,345 with Prime Factorization
| 2 | 860, 742, 105, 144, 345 |
| 2 | 430, 371, 105, 72, 345 |
| 3 | 215, 371, 105, 36, 345 |
| 5 | 215, 371, 35, 12, 115 |
| 7 | 43, 371, 7, 12, 23 |
| 43, 53, 1, 12, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 43 x 53 x 1 x 12 x 23 = 264181680
Therefore, the lowest common multiple of 860,742,105,144,345 is 264181680.
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.
860 x 742 x 105 x 144 x 345 = 3328689168000
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.
860 : 1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860
742 : 1, 2, 7, 14, 53, 106, 371, 742
105 : 1, 3, 5, 7, 15, 21, 35, 105
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
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 860,742,105,144,345, is 1.
Now, the common factors can be found like this.
860:2x 2x 5x 43
742:2x 7x 53
105:3x 5x 7
144:2x 2x 2x 2x 3x 3
345:3x 5x 23
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 5x 5x 7 = 12600
Therefore, the value for common factors is 12600.
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 = 3328689168000/(1x12600)
LCM = 3328689168000/12600
LCM = 264181680
Thus, we can understand that the LCM of 860,742,105,144,345 is 264181680.
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FAQs on LCM of 860, 742, 105, 144, 345
1. What is the LCM of 860, 742, 105, 144, 345?
Answer: LCM of 860, 742, 105, 144, 345 is 264181680.
2. How to calculate the LCM of 860, 742, 105, 144, 345?
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 860, 742, 105, 144, 345.
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}.