LCM of 460, 840, 240, 690
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 460, 840, 240, 690 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 460, 840, 240, 690. So, keep reading to learn more.
Given numbers are 460,840,240,690
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 460,840,240,690 is 38640.
Find LCM of 460,840,240,690 with Prime Factorization
| 2 | 460, 840, 240, 690 |
| 2 | 230, 420, 120, 345 |
| 2 | 115, 210, 60, 345 |
| 3 | 115, 105, 30, 345 |
| 5 | 115, 35, 10, 115 |
| 23 | 23, 7, 2, 23 |
| 1, 7, 2, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 23 x 1 x 7 x 2 x 1 = 38640
Therefore, the lowest common multiple of 460,840,240,690 is 38640.
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.
460 x 840 x 240 x 690 = 63987840000
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.
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
10 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 460,840,240,690, is 10.
Now, the common factors can be found like this.
460:2x 2x 5x 23
840:2x 2x 2x 3x 5x 7
240:2x 2x 2x 2x 3x 5
690:2x 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 2x 2x 3x 3x 5x 5x 23 = 165600
Therefore, the value for common factors is 165600.
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 = 63987840000/(10x165600)
LCM = 63987840000/1656000
LCM = 38640
Thus, we can understand that the LCM of 460,840,240,690 is 38640.
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FAQs on LCM of 460, 840, 240, 690
1. What is the LCM of 460, 840, 240, 690?
Answer: LCM of 460, 840, 240, 690 is 38640.
2. How to calculate the LCM of 460, 840, 240, 690?
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 460, 840, 240, 690.
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}.