LCM of 690, 966, 493, 140, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 690, 966, 493, 140, 312 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 690, 966, 493, 140, 312. So, keep reading to learn more.
Given numbers are 690,966,493,140,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 690,966,493,140,312 is 123821880.
Find LCM of 690,966,493,140,312 with Prime Factorization
| 2 | 690, 966, 493, 140, 312 |
| 2 | 345, 483, 493, 70, 156 |
| 3 | 345, 483, 493, 35, 78 |
| 5 | 115, 161, 493, 35, 26 |
| 7 | 23, 161, 493, 7, 26 |
| 23 | 23, 23, 493, 1, 26 |
| 1, 1, 493, 1, 26 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 23 x 1 x 1 x 493 x 1 x 26 = 123821880
Therefore, the lowest common multiple of 690,966,493,140,312 is 123821880.
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.
690 x 966 x 493 x 140 x 312 = 14353432329600
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.
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
966 : 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966
493 : 1, 17, 29, 493
140 : 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 690,966,493,140,312, is 1.
Now, the common factors can be found like this.
690:2x 3x 5x 23
966:2x 3x 7x 23
493:17x 29
140:2x 2x 5x 7
312:2x 2x 2x 3x 13
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 5x 7x 23 = 115920
Therefore, the value for common factors is 115920.
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 = 14353432329600/(1x115920)
LCM = 14353432329600/115920
LCM = 123821880
Thus, we can understand that the LCM of 690,966,493,140,312 is 123821880.
LCM of two or more Numbers Calculation Examples
Here are some samples of LCM of two or more Numbers calculations.
FAQs on LCM of 690, 966, 493, 140, 312
1. What is the LCM of 690, 966, 493, 140, 312?
Answer: LCM of 690, 966, 493, 140, 312 is 123821880.
2. How to calculate the LCM of 690, 966, 493, 140, 312?
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 690, 966, 493, 140, 312.
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}.