LCM of 224, 512, 309, 570, 690
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 224, 512, 309, 570, 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 224, 512, 309, 570, 690. So, keep reading to learn more.
Given numbers are 224,512,309,570,690
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 224,512,309,570,690 is 2419791360.
Find LCM of 224,512,309,570,690 with Prime Factorization
| 2 | 224, 512, 309, 570, 690 |
| 2 | 112, 256, 309, 285, 345 |
| 2 | 56, 128, 309, 285, 345 |
| 2 | 28, 64, 309, 285, 345 |
| 2 | 14, 32, 309, 285, 345 |
| 3 | 7, 16, 309, 285, 345 |
| 5 | 7, 16, 103, 95, 115 |
| 7, 16, 103, 19, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 16 x 103 x 19 x 23 = 2419791360
Therefore, the lowest common multiple of 224,512,309,570,690 is 2419791360.
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.
224 x 512 x 309 x 570 x 690 = 13937998233600
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.
224 : 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
512 : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
309 : 1, 3, 103, 309
570 : 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570
690 : 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 224,512,309,570,690, is 1.
Now, the common factors can be found like this.
224:2x 2x 2x 2x 2x 7
512:2x 2x 2x 2x 2x 2x 2x 2x 2
309:3x 103
570:2x 3x 5x 19
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 2x 2x 3x 3x 5 = 5760
Therefore, the value for common factors is 5760.
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 = 13937998233600/(1x5760)
LCM = 13937998233600/5760
LCM = 2419791360
Thus, we can understand that the LCM of 224,512,309,570,690 is 2419791360.
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FAQs on LCM of 224, 512, 309, 570, 690
1. What is the LCM of 224, 512, 309, 570, 690?
Answer: LCM of 224, 512, 309, 570, 690 is 2419791360.
2. How to calculate the LCM of 224, 512, 309, 570, 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 224, 512, 309, 570, 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}.