LCM of 688, 203, 120, 323, 210
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 688, 203, 120, 323, 210 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 688, 203, 120, 323, 210. So, keep reading to learn more.
Given numbers are 688,203,120,323,210
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 688,203,120,323,210 is 676672080.
Find LCM of 688,203,120,323,210 with Prime Factorization
| 2 | 688, 203, 120, 323, 210 |
| 2 | 344, 203, 60, 323, 105 |
| 2 | 172, 203, 30, 323, 105 |
| 3 | 86, 203, 15, 323, 105 |
| 5 | 86, 203, 5, 323, 35 |
| 7 | 86, 203, 1, 323, 7 |
| 86, 29, 1, 323, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 7 x 86 x 29 x 1 x 323 x 1 = 676672080
Therefore, the lowest common multiple of 688,203,120,323,210 is 676672080.
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.
688 x 203 x 120 x 323 x 210 = 1136809094400
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.
688 : 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
203 : 1, 7, 29, 203
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
323 : 1, 17, 19, 323
210 : 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 688,203,120,323,210, is 1.
Now, the common factors can be found like this.
688:2x 2x 2x 2x 43
203:7x 29
120:2x 2x 2x 3x 5
323:17x 19
210:2x 3x 5x 7
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 5x 7 = 1680
Therefore, the value for common factors is 1680.
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 = 1136809094400/(1x1680)
LCM = 1136809094400/1680
LCM = 676672080
Thus, we can understand that the LCM of 688,203,120,323,210 is 676672080.
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FAQs on LCM of 688, 203, 120, 323, 210
1. What is the LCM of 688, 203, 120, 323, 210?
Answer: LCM of 688, 203, 120, 323, 210 is 676672080.
2. How to calculate the LCM of 688, 203, 120, 323, 210?
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 688, 203, 120, 323, 210.
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}.