LCM of 240, 690, 460, 144, 320
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 240, 690, 460, 144, 320 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 240, 690, 460, 144, 320. So, keep reading to learn more.
Given numbers are 240,690,460,144,320
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 240,690,460,144,320 is 66240.
Find LCM of 240,690,460,144,320 with Prime Factorization
| 2 | 240, 690, 460, 144, 320 |
| 2 | 120, 345, 230, 72, 160 |
| 2 | 60, 345, 115, 36, 80 |
| 2 | 30, 345, 115, 18, 40 |
| 3 | 15, 345, 115, 9, 20 |
| 5 | 5, 115, 115, 3, 20 |
| 23 | 1, 23, 23, 3, 4 |
| 1, 1, 1, 3, 4 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 5 x 23 x 1 x 1 x 1 x 3 x 4 = 66240
Therefore, the lowest common multiple of 240,690,460,144,320 is 66240.
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.
240 x 690 x 460 x 144 x 320 = 3510190080000
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.
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
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
320 : 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 240,690,460,144,320, is 2.
Now, the common factors can be found like this.
240:2x 2x 2x 2x 3x 5
690:2x 3x 5x 23
460:2x 2x 5x 23
144:2x 2x 2x 2x 3x 3
320:2x 2x 2x 2x 2x 2x 5
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 2x 2x 2x 2x 2x 3x 3x 5x 5x 5x 23 = 26496000
Therefore, the value for common factors is 26496000.
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 = 3510190080000/(2x26496000)
LCM = 3510190080000/52992000
LCM = 66240
Thus, we can understand that the LCM of 240,690,460,144,320 is 66240.
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FAQs on LCM of 240, 690, 460, 144, 320
1. What is the LCM of 240, 690, 460, 144, 320?
Answer: LCM of 240, 690, 460, 144, 320 is 66240.
2. How to calculate the LCM of 240, 690, 460, 144, 320?
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 240, 690, 460, 144, 320.
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}.