LCM of 345, 706, 735, 460
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 345, 706, 735, 460 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 345, 706, 735, 460. So, keep reading to learn more.
Given numbers are 345,706,735,460
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 345,706,735,460 is 23869860.
Find LCM of 345,706,735,460 with Prime Factorization
| 2 | 345, 706, 735, 460 |
| 3 | 345, 353, 735, 230 |
| 5 | 115, 353, 245, 230 |
| 23 | 23, 353, 49, 46 |
| 1, 353, 49, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 23 x 1 x 353 x 49 x 2 = 23869860
Therefore, the lowest common multiple of 345,706,735,460 is 23869860.
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.
345 x 706 x 735 x 460 = 82351017000
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.
345 : 1, 3, 5, 15, 23, 69, 115, 345
706 : 1, 2, 353, 706
735 : 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 345,706,735,460, is 1.
Now, the common factors can be found like this.
345:3x 5x 23
706:2x 353
735:3x 5x 7x 7
460:2x 2x 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 3x 5x 5x 23 = 3450
Therefore, the value for common factors is 3450.
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 = 82351017000/(1x3450)
LCM = 82351017000/3450
LCM = 23869860
Thus, we can understand that the LCM of 345,706,735,460 is 23869860.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 345, 706, 735, 460
1. What is the LCM of 345, 706, 735, 460?
Answer: LCM of 345, 706, 735, 460 is 23869860.
2. How to calculate the LCM of 345, 706, 735, 460?
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 345, 706, 735, 460.
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}.